Lomror & Rohit attempted to solve a quadratic equation. Lomror made a mistake while noting down the constant term and got the roots as 4 & 3. Rohit made a mistake while noting down the coefficient of x and got the roots as 2 & 3. Find the roots of the actual quadratic equation.
Explanation:
We know, in a quadratic equation ax2 + bx + c = 0,
Sum of the roots = -b/a and product of the roots = c/a
Lomror wrote the contant term wrong but he wrote the coefficient of x correctly, hence the sum of the roots he got would be same as the sum of the roots of the actual equation.
∴ Sum of the roots of the actual equation = 4 + 3 = 7
Rohit wrote the coefficient of x wrong but he wrote the constsant term correctly, hence the product of the roots he got would be same as the product of the roots of the actual equation.
∴ Product of the roots of the actual equation = 2 × 3 = 6
Hence, the original equation is x2 - 7x + 6 = 0.
⇒ (x - 6)(x - 1) = 0
⇒ x = 1 or 6.
Hence, option (c).
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