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Standard X

Mathematics

Quadratic Formula

Equation x2...

Question

Equation $x^{2} - x + q = 0$ has imaginary roots if

q > \frac{1}{4}

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q < \frac{1}{4}

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q^{2} < \frac{1}{4}

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None of these

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Solution

The correct option is A $q > \frac{1}{4}$
$x^{2} - x + q = 0$
It has imaginary roots, if
$D < 0$
$b^{2} - 4 a c < 0$
$(1)^{2} - 4 (1) (q) < 0$
$1 < 4 q$
$\frac{1}{4} < q$
$∴ q > \frac{1}{4}$

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If $α$ be a real root of the equation $x^{3} + p x^{2} + q x + r = 0$ where p, q and r are real. If $p^{2} - 4 q - 2 p α - 3 α^{2} \geq 0$ then other roots are ________.

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Equation x2−x+q=0 has imaginary roots if

The correct option is A q>14x2−x+q=0It has imaginary roots, ifD<0b2−4ac<0(1)2−4(1)(q)<01<4q14<q∴q>14

Equation $x^{2} - x + q = 0$ has imaginary roots if

The correct option is A $q > \frac{1}{4}$
$x^{2} - x + q = 0$
It has imaginary roots, if
$D < 0$
$b^{2} - 4 a c < 0$
$(1)^{2} - 4 (1) (q) < 0$
$1 < 4 q$
$\frac{1}{4} < q$
$∴ q > \frac{1}{4}$