Question

5. If the roots of the equation ax2 + bx + c = 0 are equal, then x = ? b b (a) (b) 2a 4a 5 (c) (d) 62 2a 2a​

Answer 1

$\huge \boxed{(c) - \frac{b}{2a} }$

Step-by-step explanation:

QUESTION :-

if the roots of the equation ax² + bx + c = 0 are equal, then x = ?

a) $\frac{b}{2a}$

b) $\frac{b}{4a}$

c) $- \frac{b}{4a}$

d) $- \frac{{b}^{2}}{2a}$

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SOLUTION :-

As we know roots of the equation ax² + bx + c = 0 is

$x = \frac{-b ± \sqrt{{b}^{2} - 4ac}}{2a}$

When Discriminant (b² - 4ac) = 0, the roots will be equal, so for this case

$x = \frac{-b ± \sqrt{{b}^{2}-4ac}}{2a} \\ \\ => x = \frac{-b±\sqrt{0}}{2a} \\ \\ => x = \frac{-b ± 0}{2a} \\ \\ => x = \frac{-b}{a}$

So,

our answer will be option (c)

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More to know :-

• A quadratic have only two roots.
• The roots of equation can be found by the quadratic formula (Sridharacharya formula) -

$\frac{-b ± \sqrt{{b}^{2}-4ac}}{2a}$

When the Discriminant (b² - 4ac),

• D < 0, then roots will be imaginary
• D = 0, then roots will be real and equal
• D > 0, then roots will be real and unequal

• Sum of both roots = -b/a
• Product of zeroes = c/a

hope it helps.

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