A real number - is said to be a root of a x2-b x-c-0

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Standard XII

Mathematics

Squaring an Inequality

A real number...

Question

A real number α is said to be a root of ax²+bx+c =0

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Solution

The correct option is A

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Similar questions

Q. A real number

α

is said to be the root of the quadratic equation

a x^{2} + b x + c = 0

, if

a α^{2} + b α + c = 0

Let a, b, c be real numbers a $\neq$ 0. If $α$ is a root of $a^{2} x^{2}$ + bx + c = 0, $β$ is a root of $a^{2} x^{2}$ - bx - c = 0 and 0 < $α < β$ , then the equation $a^{2} x^{2}$ + 2bx + 2c = 0 has a root $γ$ that always satisfies

Q. If

α, β

are real and distinct roots of

a x^{2} + b x - c = 0

and

p, q

are real and distinct roots of

a x^{2} + b x - | c | = 0

, where

(a > 0)

, then

Q. Let

a, b, c

be real numbers with

a \neq 0

and let

α, β

be the roots of the equation

a x^{2} + b x + c = 0

. Express the roots of

a^{3} x^{2} + a b c x + c^{3} = 0

in terms of

α, β

Q. If both the roots

α, β

of the quadratic equation

a x^{2} + b x + c = 0, a < 0

are less than a real number

k

such that

k > α > β

Considering

f (x) = a x^{2} + b x + c

, select the correct statement(s).

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A real number α is said to be a root of ax2+bx+c =0

The correct option is A

A real number α is said to be a root of ax²+bx+c =0