If $b^{2} - 4 a c > 0$ in $a x^{2} + b x + c = 0$ , then what can you say about roots of the equation? ( $a \neq 0$ )

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Solution

Given $b^{2} - 4 a c > 0$ and $a \neq 0$ ,
Roots of $a x^{2} + b x + c = 0$ will be given by $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , as quantity under square-root is positive, roots will be rational and distinct.

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Similar questions

Q. If

b^{2} - 4 a c \geq 0

then the roots of quadratic equation

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

is-

Q. What is the nature of the roots of the quadratic equation

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

if
(a)

b^{2} - 4 a c = 0

(b)

b^{2} - 4 a c < 0

Q. If

b^{2} - 4 a c \geq 0

, then write the nature of roots of a quadratic equation

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

The roots of a quadratic equation $a x^{2} + b x + c = 0$ are given by $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , provided $b^{2} - 4 a c \geq 0$ .

Q. If the roots of

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

are

α, β

and the roots of

A X^{2} + B x + C = 0

are

(α - k), (β - k)

. Then

(\frac{B^{2} - 4 A C}{b^{2} - 4 a c})

is equal to

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If b2−4ac>0 in ax2+bx+c=0, then what can you say about roots of the equation? (a≠0)

Given b2−4ac>0 and a≠0,Roots of ax2+bx+c=0 will be given by −b±√b2−4ac2a, as quantity under square-root is positive, roots will be rational and distinct.

If $b^{2} - 4 a c > 0$ in $a x^{2} + b x + c = 0$ , then what can you say about roots of the equation? ( $a \neq 0$ )

Given $b^{2} - 4 a c > 0$ and $a \neq 0$ ,
Roots of $a x^{2} + b x + c = 0$ will be given by $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , as quantity under square-root is positive, roots will be rational and distinct.