Quadratic Equations - Algebra - Mathematics Previous Year Questions

Let x₁ and x₂ be the real roots of the equation \({x^2} - (k - 2)x + ({k^2} + 3k + 5) = 0\), then maximum value of \(x_1^2 + x_2^2\) is

When x¹⁰⁰ is divided by x² \(-\) 3x + 2, the remainder is (2^{k + 1} \(-\) 1)x \(-\)(2^k \(-\) 1), then k is

If a\(\in\)R, b\(\in\)R, then the equation x² \(-\) abx \(-\) a² = 0 has

The solution of the inequality \({4^{ - x + 0.5}} - {7.2^{ - x}} < 4\), x \(\in\)R is

Let a, b be the solutions of x² + px + 1 = 0 and c, d be the solution of x² + qx + 1 = 0. If (a \(-\) c) (b \(-\) c) and (a + d)(b + d) are the solution of x² + ax + \(\beta\) = 0, then \(\beta\) is equal to

If \(\alpha\) be a root of the equation \(4{x^2} + 2x - 1 = 0\), then the other root of the equation is

Let \(\alpha, \beta\) be the roots of the equation \(x^2-p x+r=0\) and \(\frac{\alpha}{2}, 2 \beta\) be the roots of the equation \(x^2-q x+r=0\). Then, the value of \(r\) is equal to

If \(\alpha<1\) be a root of the equation \(2 x^2-5 x+2=0\), then the other root of the equation is

For what value of $a, 6$ lies between the roots of the equation $x^2+2(a-3) x+9=0$.

Roots of the equation $a x^2+b x+c=0(a, b, c>0)$ are