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.
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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
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Verified answer
Given quadratic equation:-
Roots:-
Now ,
Sum of roots = [tex]\frac{–43}{17}[/tex]
→ A + B = [tex]\bold{\frac{–43}{17}}[/tex] ——(i)
And Product of roots = [tex]\frac{–73}{17}[/tex]
→ AB = [tex]\bold{\frac{–73}{17}}[/tex] —— (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