Question

if b Square - 4ac =0, write the nature of roots of the quadratic equation ax square +bx +c=0​

Answer 1

Question

if b² - 4ac =0, write the nature of roots of the quadratic equation ax² +bx +c=0

Topic

Nature of Roots

Solution

Let ax²+bx+c=0, a≠0 be a quadratic equation.

Suppose D=b²-4ac=0 i.e the discriminant of the equation is zero, the equation has real and equal roots.

$\sf \implies{x = \dfrac{-b+\sqrt D}{2a} \: or \: \dfrac{-b-\sqrt D}{2a} }$

$\sf \implies{x = \dfrac{-b+0}{2a} \: or \: \dfrac{-b-0}{2a} }$

$\sf \implies{ \red{x= \dfrac{-b}{2a}}}$

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More to know !!

$\mathtt{If \: D=b²-4ac > 0}$

• discriminant of the equation is positive then the equation has real and distinct roots.

$\mathtt{If \: D=b²-4ac < 0}$

• the discriminant of the quadratic equation is negative then the equation has no real roots.

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