If the following quadratic equation has two e | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For a quadratic equation of the form $ax^{2} + bx + c = 0$,the roots are equal and real if the discriminant $D = b^{2} - 4ac = 0$.Given the equati

Vedclass · Accepted Answer

$51$

Vedclass · Answer

(C) For a quadratic equation of the form $ax^{2} + bx + c = 0$,the roots are equal and real if the discriminant $D = b^{2} - 4ac = 0$.Given the equation: $16x^{2} - 40x + \frac{k-1}{2} = 0$.Here,$a = 16$,$b = -40$,and $c = \frac{k-1}{2}$.Substituting these values into the discriminant formula:$(-40)^{2} - 4(16)\left(\frac{k-1}{2}\right) = 0$$1600 - 64\left(\frac{k-1}{2}\right) = 0$$1600 - 32(k-1) = 0$$1600 - 32k + 32 = 0$$1632 = 32k$$k = \frac{1632}{32} = 51$.Thus,the value of $k$ is $51$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $16x^{2} - 40x + \frac{k-1}{2} = 0$.

Similar Questions

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $9x^2 + 6x + 4 = 0$.

The value of the discriminant of the quadratic equation $5x^{2} + x + 2 = 0$ is ..... .

The value of the discriminant of the quadratic equation $x^{2}-8x+15=0$ is ...... .

State whether the quadratic equation $(x+4)^{2}-8x=0$ has two distinct real roots. Justify your answer.

The value of the discriminant of the quadratic equation $4x^{2} + 20x + 25 = 0$ is $\ldots \ldots \ldots \ldots .$

Vedclass Test Series

Exam Paper Generator

Online Exam Module