Question

The roots of equation ax² +bx+c =0,a is not equal to 0 are equal then the roots are
1) -b/a ,-b/a 2) c/a,c/a
3) -b/2a,-b/2a 4) c/2a,c/2a

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Answer 1

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } GiveN:-}}}}}$

• The roots of quadratic equⁿ ax² + bx + c are equal .
• a is not equal to 0 . ( a ≠ 0 ) .

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } To\:FinD:-}}}}}$

• The roots of the quadratic equation.

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } FormulA\:UseD:-}}}}}$

$\sf{ We \:will \:use}\: \bf"Quadratic formula ":-$

$\large\orange{\underline{\boxed{\green{\tt{\blue{\dag } x\:\:=\:\:\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}}}}}$

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } AnsweR:-}}}}}$

Given quadratic equation to us is : ax²+bx+c = 0 .

$\tt Have\:a\:look\:at\:this\:table:$

$\boxed{\begin{tabular}{|c|c|} \cline{1-2} \bf Condition & \bf Nature of Roots \\ \cline{1-2} \sf D>0 &\sf Roots are real \\ \cline{1-2} \sf D=0 & Roots are equal \\ \cline{1-2} \sf D<0 & \sf Roots are complex (Imaginary) \\ \cline{1-2}\end{tabular}}$

From the table it is clear that if the roots are equal then Discriminant = 0 .

Now, put this value in " Quadratic formula " ,

$\tt:\implies x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\tt:\implies x=\dfrac{-b\pm\sqrt{0}}{2a}$

$\tt:\implies x=\dfrac{-b+0}{2a}\:,\:\dfrac{-b-0}{2a}$

$\underline{\boxed{\red{\tt{\longmapsto \:\:x\:\:=\:\:\dfrac{-b}{2a}\:\:,\:\:\dfrac{-b}{2a}}}}}$

$\orange{\boxed{\purple{\bf{\dag Hence\: correct\: option\:is\:[3].}}}}$