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
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 = 11. If α and β are the root of x2 + 32x + 200 then find the value of α/β + β/α.
2. What is the difference of the factors of the expression $x^{2}+ \left(\frac{1}{x^{2}}\right) - 6$
4. What is the value of $\frac{(4a^{2} + 8b + 14c + 2)}{2}$ ?
6. If 2x - 1 < 5x + 2 and 2x + 5 < 6 - 3x, then x can take which of the following values?
9. If (x/5) + (5/x) = – 2, then what is the value of x3?
10. If 4(x + 5) - 3 > 6 - 4x ≥ x - 5Íž Then the value of x is