Question

if the roots of the quadratic equation 4x²+12x+c=0 are equal, then the value of c?
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Answer 1

EXPLANATION.

Roots of the quadratic equation.

F(x) = 4x² + 12x + c = 0. are equal.

As we know that,

if roots are real and equal,

⇒ D = 0 Or b² - 4ac = 0.

⇒ (12)² - 4(4)(c) = 0.

⇒ 144 - 16c = 0.

⇒ 144 = 16c.

⇒ c = 144/16.

⇒ c = 9.

                                                                                     

MORE INFORMATION.

Nature of the factors of the quadratic expression,

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = if D < 0 Roots are imaginary and unequal or complex conjugate.

Answer 2

$\\ \\ \large \color{blue}\underline{\sf \: Question :- }$

If the roots of the quadratic equation 4x²+12x+c=0 are equal, then the value of c?

$\\ \\ \large \color{blue}\underline{\sf \: Answer :- }$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \longrightarrow \: The \: value \: of \: c \: is \: 9 .$

$\\ \\ \large\color{blue}\underline{\sf \: Solution :- }$

$\\ \sf \: Here,$

$\\ \\ \sf \: Given \: that$

$\sf \: the \: roots \: of \: the \: quadratic \: equation \: 4x²+12x+c=0 \: are \: equal,$

$\\ \\ \sf \: So , \: we \: know \: this$

$\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: If \: the \: roots \: are \: real \: and \: equal \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf\: then \: the \: value \: of \: determinat \: i s \: 0$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: {b}^{2} - 4ac \: = 0$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: {12}^{2} - 4 \times 4 \times c \: = 0$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: {144} - 16\times c \: = 0$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: {144} - 16 c \: = 0$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: 16 c \: = 144$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: c \: = \frac{144}{16}$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: \underline{ \boxed{ \orange {\tt c \: = 9} }}$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \: \: \: \: : Hence, \: the \: value \: of \: c \: is \: 9 . \: \: }$