Question

if A and B are the roots of the quadratic equation 17x2 + 43x - 73 = 0, construct a quadratic equation whose roots are A + 2 and B + 2.
find me the answer​

Answer 1

Given quadratic equation:-

• 17x² + 43x - 73 = 0

Roots:-

• A and B

Now ,

Sum of roots = $\frac{–43}{17}$

→ A + B = $\bold{\frac{–43}{17}}$ ——(i)

And Product of roots = $\frac{–73}{17}$

→ AB = $\bold{\frac{–73}{17}}$ —— (ii)

To find:- Quadratic equation with roots (A+2) and (B+2) .

∴ Sum of roots

= A + 2 + B + 2

= A + B + 4

= (-43/17) + 4 { from eqn (i) }

= 25/17

And Product of roots

= (A+2)(B+2)

= AB + 2A + 2B + 4

= (-73/17) + 2(A + B) + 4

= (-73/17) + 2 (-43/17) + 4

= -91/17

∴ Quadratic equation with roots (A + B) and

(B + 2) ,

» x² - {(A + 2) + (B + 2)}x + (A+2)(B+2) = 0

→ x² - (25/17)x - (91/17) = 0

→ 17x² - 25x - 91 = 0