OE


It is given that while noting down a quadratic equation Lauren noted the coefficient
of 𝑥 incorrectly and got the roots 7 and -2, whereas Harry noted the same equation
and noted constant term incorrectly and got the roots of the equation as -11 and 6.
We need to compare
Quantity A: Larger of the two roots of actual quadratic equation
Quantity B: 3
Now, the standard form of quadratic equation is 𝑦 = a𝑥
2 + 𝑏𝑥 + 𝑐, where 𝑎 ≠ 0 and
𝑏 and 𝑐 are constants.
Since, Lauren got 𝑏 wrong and the roots are 7 and -2 so the equation becomes 𝑦 =
(𝑥 − 7)(𝑥 + 2)

i.e. 𝑦 = 𝑥^2 − 5𝑥 − 14

Since, 𝑏 is wrong so the actual equation has 𝑎 = 1 and 𝑐 = -14.
Similarly, Harry got 𝑐 wrong and got the roots -11 and 6 so the equation is 𝑦 = (𝑥 + 11)(𝑥 − 6)
i.e. y = 𝑥^2 + 5𝑥 − 66
Since, 𝑐 is wrong so the actual equation has 𝑎 = 1 and 𝑏 = 5.
Hence, the original equation is 𝑦 = 𝑥
2 + 5𝑥 − 14.
Factorizing we get, 𝑥^2 + 7𝑥 − 2𝑥 − 14 = 0
i.e. 𝑥(𝑥 + 7) − 2(𝑥 + 7) = 0
i.e. (𝑥 + 7)(𝑥 − 2) = 0
i.e. 𝑥 = − 7 or 𝑥 = 2
Hence the larger of the two roots is 2.