Question

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

Answer 1

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