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A and B solved a quadratic equation. In solving it, A made a mistake in the constant term and obtained the roots as 6 and 2, while B made a mistake in the coefficient of x only and obtained the roots as -7 and -1. Find the correct roots of the equation?

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A and B solved a quadratic equation. In solving it, A made a mistake in the constant term and obtained the roots as 6 and 2, while B made a mistake in the coefficient of x only and obtained the roots as -7 and -1. Find the correct roots of the equation?
1). 2 or 1
2). 3 or 4
3). 5 or 6
4). 7 or 1


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1 answers

2 vote
Answered by on | Votes 2 |

A quadratic equation is given as,

x2 – (a + b)x + ab = 0 where a and b are the roots of the given quadratic equation

According to the given condition,

For A the equation is

x2 – (6 + 2)x + 12 = 0

The coefficient of ‘x’ for A’s equation is correct

So, Coefficient of ‘x’ = -8

For B the equation is

$({x^2} - \left( { - 7 - 1} \right)x + \left( { - 7 \times - 1} \right) = \;0)$

$(\therefore {x^2} + 8x + 7 = 0)$

The constant term for B’s equation is correct

So, constant term = 7

∴ The correct equation will be,

$({x^2} - 8x + 7 = 0)$

On solving this equation, we get:

∴ x = 7 or x = 1

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