Question

the roots equation of 9x2-bx+81=0 will be equal if the value of b is
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Answer 1

$\Large\underline\mathfrak{Question}$

• Roots of Equation 9x² -bx + 81 = 0 are Equal .
• Find value of b ?

$\Large\bold\star\underline{\underline\textbf{Concept\:used}}$

If A•x^2 + B•x + C = 0 ,is any quadratic equation,

then its discriminant is given by;

D = B^2 - 4•A•C

• If D = 0 , then the given quadratic equation has real and equal roots.

• If D > 0 , then the given quadratic equation has real and distinct roots.

• If D < 0 , then the given quadratic equation has unreal (imaginary) roots.

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$\underline {\underline{\LARGE{{\bf{\green{S}}}{\mathfrak{o}}{\mathfrak{\orange{l}}}{\mathfrak{\red{u}}}{\mathfrak{\pink{t}}}{\mathfrak{\purple{i}}}{\mathfrak{\blue{o}}}{\mathfrak{\red{n}}}}}} : \:$

Here ,

→ a = 9

→ b = (-b)

→ c = 81 .

Since Roots are Equal ..

Than , b²-4ac = 0 ,

putting values now we get,

$\red{\bf \: ( - b)^{2} - 4 \times 9 \times 81 = 0} \\ \\ \red\longrightarrow \green{\sf \: {b}^{2} = 4 \times 9 \times 9 \times 9} \\ \\ \red\longrightarrow \purple{\bf \: b = \sqrt{2 \times 2 \times 9 \times 9 \times 3 \times 3}} \\ \\ \red\longrightarrow \sf \: b = 2 \times 9 \times 3 \\ \\ \pink{\large\boxed{\boxed{\bold{ \green{b} \blue= \orange{54}}}}}$

Hence , value of b is 54....

#BAL

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