(A) To determine the nature of the roots of the quadratic equation $ax^2 + bx + c = 0$,we calculate the discriminant $D = b^2 - 4ac$.Here,$a = 9$,$b =

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(A) To determine the nature of the roots of the quadratic equation $ax^2 + bx + c = 0$,we calculate the discriminant $D = b^2 - 4ac$.Here,$a = 9$,$b = 30$,and $c = 25$.Substituting these values into the discriminant formula:$D = (30)^2 - 4(9)(25)$$D = 900 - 900$$D = 0$Since the discriminant $D = 0$,the quadratic equation has real and equal roots.

Class 10 Mathematics Quadratic Equations Mix Examples - Quadratic Equations

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The equation $9x^2 + 30x + 25 = 0$ has .............. in $R$.

A
equal roots
B
unequal roots
C
no roots
D
irrational roots

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Mix Examples - Quadratic Equations

The sum of two numbers is $15$. If the sum of their reciprocals is $\frac{3}{10}$,then find the numbers.

Medium

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Examine whether the following equation is quadratic or not: $x^{3}-4x^{2}-x+1=(x-2)^{3}$

Easy

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If one of the roots of $2x^{2}-5x+k=0$ is $\frac{7}{2}$,then $k=$ .............

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If the discriminant $D = 0$,then the roots of the quadratic equation $ax^2 + bx + c = 0$ are ..... .

Medium

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Obtain the roots of the following quadratic equation by using the quadratic formula: $9x^{2} + 7x - 2 = 0$.

Easy

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The equation $9x^2 + 30x + 25 = 0$ has .............. in $R$.

Similar Questions

The sum of two numbers is $15$. If the sum of their reciprocals is $\frac{3}{10}$,then find the numbers.

Examine whether the following equation is quadratic or not: $x^{3}-4x^{2}-x+1=(x-2)^{3}$

If one of the roots of $2x^{2}-5x+k=0$ is $\frac{7}{2}$,then $k=$ .............

If the discriminant $D = 0$,then the roots of the quadratic equation $ax^2 + bx + c = 0$ are ..... .

Obtain the roots of the following quadratic equation by using the quadratic formula: $9x^{2} + 7x - 2 = 0$.

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