Question

यदि द्विघात समीकरण aएक्स स्क्वायर प्लस बी एक्स प्लस सी बराबर 0 के मूल बराबर हो तो सी का मान होगा ​

Answer 1

SOLUTION

GIVEN

The roots of the quadratic equation ax² + bx + c = 0 are equal

TO DETERMINE

The value of c

EVALUATION

Here the given Quadratic equation is

ax² + bx + c = 0

Now it is given that the roots are equal

Let the roots are m , m

Then

$\displaystyle \sf{m + m = - \frac{b}{a} }$

$\displaystyle \sf{ \implies \: 2 m = - \frac{b}{a} }$

$\displaystyle \sf{ \implies \: m = - \frac{b}{2a} }$

Again

$\displaystyle \sf{ \: m \times m = \frac{c}{a} }$

$\displaystyle \sf{ \implies \: {m}^{2} = \frac{c}{a} }$

Putting the value of m we get

$\displaystyle \sf{ { \bigg( - \frac{b}{2a} \bigg)}^{2} = \frac{c}{a} }$

$\displaystyle \sf{ \implies \: \frac{ {b}^{2} }{4 {a}^{2} } = \frac{c}{a} }$

$\displaystyle \sf{ \implies \: {b}^{2} = 4 {a}^{2} \times \frac{c}{a} }$

$\displaystyle \sf{ \implies \: {b}^{2} = 4ac }$

$\displaystyle \sf{ \implies \: c = \frac{ {b}^{2} }{4a} }$

FINAL ANSWER

$\boxed{ \: \: \displaystyle \sf{ c = \frac{ {b}^{2} }{4a} } \: \: \: }$

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