If alpha beta are the roots of the equation

Asked by admin @ in Math viewed by 296 People

If alpha,beta are the roots of the equation x^2-3x+2=0 then the equation whose roots are (alpha+1) and (beta+1) is

a) x^2+5x+6=0 b) x^2-5x-6=0
c)x^2+5x-6=0 c)x^2-5x+6

Answered by admin @


AnswEr

The correct option is

d)x² - 5x + 6 = 0

Given

The quadratic equation

  • x² - 3x + 2 = 0
  • roots of the above equation are α and β

To Find

The equation whose roots are (α+1) and (β+1)

Solution

We know that

Sum of the roots = -coefficient of x/coefficient of x²

⇒α + β = -(-3)/1

⇒α + β = 3

And product of the roots = constant term/coefficient of x²

⇒αβ= 2/1

⇒αβ= 2

Since we have to find the equation whose roots are (α+1) and (β+1)

So the new equation will be

x² - [(α+1)+( β+1)]x + (α+1)(β+1)=0

So the sum of the new roots is

α + 1 +β + 1

= α + β + 2

= 3+ 2 ( since α + β = 3)

= 5

And the product of the new roots is

(α+1)(β+1)

=αβ + α + β + 1

= 2 + 3+ 1

= 6

Therefore the required equation is

x² -(5)x + (6) = 0

⇒x² - 5x + 6 = 0


Similar Questions

What are the symbols for alpha beta and gamma radiation

Asked by admin @ in Biology viewed by 280 persons

Match the radiation with its symbol. 1. beta 2. gamma 3. alpha

Alpha cells and beta cells can be found in the

Asked by admin @ in Biology viewed by 283 persons

Alpha cells are to ________ as beta cells are to ________.

How to solve equations with square roots on both sides

Asked by admin @ in Mathematics viewed by 320 persons

Help!!! PLEASE :( What is the first step in solving quadratic equations by finding square roots? a.give the positive and negative answer   c.square root both sides to isolate x^2   b.isolate …

How are gamma rays different from alpha and beta particles

Asked by admin @ in Physics viewed by 356 persons

How does gamma radiation differ from alpha or beta particle radiation? A.) it does not consist of matter B.) it does not consist of energy C.) it only consists of …

Explain the main differences between alpha beta and gamma rays

Asked by admin @ in Chemistry viewed by 320 persons

Differentiate between alpha and beta and gamma rays

If alpha and beta are zeros of polynomial

Asked by admin @ in Math viewed by 343 persons

if alpha and beta are the zeros of a quadratic polynomial such that alpha + beta is equals to 24 and Alpha minus beta is equal to 8 find the …

If alpha and beta are solutions of acostheta bsintheta

Asked by admin @ in Math viewed by 321 persons

if alpha and beta are two distinct roots satisfying the equation acostheta +bsintheta =c prove that sin (alpha+beta) =2ab/asquare+bsquare

If alpha and beta are two different complex numbers

Asked by admin @ in Math viewed by 419 persons

Question 17 If α and β are different complex numbers with | β |= 1, then find | (β-α)/(1- αβ) |. Class X1 - Maths -Complex Numbers and Quadratic Equations …

If the sum of the roots of the equation

Asked by admin @ in Math viewed by 295 persons

If the sum of the roots of the quadratic equation ax2+bx+c=0 is equal to the sum of the squares of their reciprocals then b2/ac + bc/a2 is equal to

Determine if 3 is a root of the equation

Asked by admin @ in Math viewed by 347 persons

Determine, if 3 is a root of the equation given below √x2-4x+3+√x2-9=√4x2-14x+16

If alpha and beta are zeros of quadratic polynomial

Asked by admin @ in Math viewed by 318 persons

if alpha and beta are the zeros of a quadratic polynomial such that alpha + beta is equals to 24 and Alpha minus beta is equal to 8 find the …

If a and b are roots of the equation

Asked by admin @ in Math viewed by 318 persons

If a and b are roots of quadratic equation x2+ax+b=0 then find the values of a and b.

If alpha beta are the zeros of the polynomial

Asked by admin @ in Math viewed by 341 persons

If alpha and beta are the zeroes of the polynomial x^2-3x+k , such that alpha-beta=1, find the value of k

Alpha and beta are the zeros of the polynomial

Asked by admin @ in Math viewed by 345 persons

If alpha and beta are the zeroes of the polynomial x^2-3x+k , such that alpha-beta=1, find the value of k

If alpha and beta are the zeros of polynomial

Asked by admin @ in Math viewed by 333 persons

if alpha and beta are the zeros of a quadratic polynomial such that alpha + beta is equals to 24 and Alpha minus beta is equal to 8 find the …

Most viewed questions in Math

What is the value of x in the expression

Asked by admin @ in Math viewed by 15188 persons

Shubham is facing south and moves 30 km

Asked by admin @ in Math viewed by 12992 persons

Prachi excellence in mathematics class 7 solutions pdf free download

Asked by admin @ in Math viewed by 12072 persons

Oxford new enjoying mathematics class 7 solutions chapter 1

Asked by admin @ in Math viewed by 11543 persons

Survey of various types of bank accounts icse project

Asked by admin @ in Math viewed by 11519 persons

The town of p is located at point x

Asked by admin @ in Math viewed by 11367 persons

A clock gains 4 minutes after every 4 minutes

Asked by admin @ in Math viewed by 10182 persons

Running a tuck shop or canteen maths project pdf

Asked by admin @ in Math viewed by 9407 persons

Paul is sixteenth from the front of the row

Asked by admin @ in Math viewed by 9360 persons

The average weight of 20 teachers is 80 kg

Asked by admin @ in Math viewed by 7531 persons

The number 567 xy is completely divisible by 30

Asked by admin @ in Math viewed by 7410 persons

In a row of friends tiya occupies fifteenth place

Asked by admin @ in Math viewed by 7213 persons

What would $ mean if fat is coded as

Asked by admin @ in Math viewed by 5284 persons

Consider a 3 digit integer x with distinct digits

Asked by admin @ in Math viewed by 4813 persons

Rahul went to his mother's mother in law

Asked by admin @ in Math viewed by 4187 persons