(C) For a quadratic equation $ax^2 + bx + c = 0$,the discriminant $D$ is given by $D = b^2 - 4ac$.If the roots of the quadratic equation are equal,the

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(C) For a quadratic equation $ax^2 + bx + c = 0$,the discriminant $D$ is given by $D = b^2 - 4ac$.If the roots of the quadratic equation are equal,then the discriminant must be equal to zero,i.e.,$D = 0$.Substituting the value of $D$,we get $b^2 - 4ac = 0$.Therefore,$b^2 = 4ac$.

Class 10 Mathematics Quadratic Equations Mix Examples - Quadratic Equations

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If both the roots of a quadratic equation $ax^2 + bx + c = 0$ $(a \neq 0)$ are equal,then ..... .

A
$a = c$
B
$a^2 = 4bc$
C
$b^2 = 4ac$
D
$c^2 = 4ab$

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Mix Examples - Quadratic Equations

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $x^{2}+6x+5=0$.

Medium

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Find whether the following equation has real roots. If real roots exist,find them.
$x^{2}+5 \sqrt{5} x-70=0$

Medium

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Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

Easy

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Find the roots of the following quadratic equation by the method of completing the square: $4x^{2} + 20x + 23 = 0$.

Medium

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The sum of squares of two consecutive odd numbers is $514$. Find those numbers.

Difficult

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If both the roots of a quadratic equation $ax^2 + bx + c = 0$ $(a \neq 0)$ are equal,then ..... .

Similar Questions

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $x^{2}+6x+5=0$.

Find whether the following equation has real roots. If real roots exist,find them.$x^{2}+5 \sqrt{5} x-70=0$

Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

Find the roots of the following quadratic equation by the method of completing the square: $4x^{2} + 20x + 23 = 0$.

The sum of squares of two consecutive odd numbers is $514$. Find those numbers.

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Find whether the following equation has real roots. If real roots exist,find them.
$x^{2}+5 \sqrt{5} x-70=0$