If α and β are the roots of the equation x + a + b = abx, then what is (αβ + α + β) equal to?
ab - a - b
By analyzing the given equation and solving for the values of αβ + α + β, the correct answer is found to be (b) ab - a - b.
If x = 2 + 2 2/3 + 2 1/3 , then what is the value of x 3– 6x 2+ 6x?
If \(\sqrt {\frac{{\rm{x}}}{{\rm{y}}}} = \frac{{24}}{5} + \sqrt {\frac{{\rm{y}}}{{\rm{x}}}} \) and x + y = 26, then what is the value of xy?
If α and β are the roots of the equation x 2+ px + q = 0, then what is α 2+ β 2equal to?
If α and β are the roots of the quadratic equation 2x 2+ 6x + k = 0, where k < 0, then what is the maximum value of (α/β + β/α)?
If 4x + 3a = 0, then what is the value of \(\frac{{{x^2}\; + \;ax\; + \;{a^2}}}{{{x^3} - {a^3}}} - \;\frac{{{x^2} - \;ax\; + \;{a^2}}}{{{x^3}\; + \;{a^3}}}\;\) ?
If p and q are the roots of x 2+ px + q = 0, then which of the following is correct?
It is given that the equations x 2– y 2= 0 and (x – a) 2+ y 2= 1 have single positive solution. For this, the value of ‘a’ is
The sum of all real values of x satisfying the equation
\(\rm (x^2 - 5x + 5) ^{x^2 + 4x - 60 }= 1\) is:
The number of integral values of $m$ for which the quadratic expression, $(10m-9)x^2 - 2mx + 1$, where $x \in \mathbb{R}$, is always positive, is
For a quadratic equation, ax 2+ bx + c = 0, if b 2– 4ac = 0, then the roots are,
If x + y + z = 0, then what is the value of \(\frac {x} {(yz)^2}+ \frac {y} {(xz)^2} + \frac {z} {(xy)^2}\)?