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Two candidates attempt to solved a quadratic equation of from x2 + px + q = 0. One starts with a wrong value of p and finds the roots to be 2 and 6. Other starts with a wrong value of q and find the root to be 2 and -9. Find the correct roots and equation ?
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- -3, -2 and x x2 + 9x + 18
- 3, 4 and x2 + 8x + 15
- -3, -4 and x2 + 7x + 12
- 2, 6 and x2+ 7x + 12
Correct Option: C
When p is wrong i.e., -b/a = (α + β) is wrong but c/a =(αβ) is correct.
Then αβ = c/a = 2 x 6 = 12 ....(i)
Again, when q is wrong i.e.,c/a = (α.β ) is wrong but -b/a = α+β is correct.
Then, -b/a = α+β= 2 + (-9) = -7
So, the required correct quadratic equations is
x2 -(α + β)x + α.β=0
⇒ x2 - (-7)x + 12 = 0
⇒ x2 + 7x + 12 = 0
and correct roots this equations are -3, -4.
