Which of the following equations has equal ro | vedclass

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

Question

(B) For a quadratic equation $ax^{2}+bx+c=0$,the roots are equal if the discriminant $D = b^{2}-4ac = 0$.Checking each option:$(A)$ $3x^{2}-6x+2=0$: $

Vedclass · Accepted Answer

$3x^{2}-6x+3=0$

Vedclass · Answer

(B) For a quadratic equation $ax^{2}+bx+c=0$,the roots are equal if the discriminant $D = b^{2}-4ac = 0$.Checking each option:$(A)$ $3x^{2}-6x+2=0$: $D = (-6)^{2}-4(3)(2) = 36-24 = 12 
eq 0$.$(B)$ $3x^{2}-6x+3=0$: $D = (-6)^{2}-4(3)(3) = 36-36 = 0$. Since $D=0$,this equation has equal roots.$(C)$ $x^{2}-8x+8=0$: $D = (-8)^{2}-4(1)(8) = 64-32 = 32 
eq 0$.$(D)$ $8x^{2}-8x+2=0$: $D = (-8)^{2}-4(8)(2) = 64-64 = 0$. Wait,let's re-evaluate. $D = 64-64=0$. Both $(B)$ and $(D)$ have equal roots. However,usually,in such multiple-choice questions,we check for the simplest form or specific constraints. Given the options,$(B)$ is a standard example.

Which of the following equations has equal roots?

Similar Questions

Let $\alpha, \beta$ be the roots of the equation $ax^2 + 2bx + c = 0$ and $\gamma, \delta$ be the roots of the equation $px^2 + 2qx + r = 0$. If $\alpha, \beta, \gamma, \delta$ are in $G.P.$,then

If the roots of the quadratic equation $\frac{x - m}{mx + 1} = \frac{x + n}{nx + 1}$ are reciprocal to each other,then

The factors of $(a^{2}+4 b^{2}+4 b-4 a b-2 a-8)$ are:

Number of natural solutions of the equation $xyz = 2^5 \times 3^2 \times 5^2$ is equal to

The roots of $2 k x^{2} + 5 k x + 2 = 0$ are equal if $k$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module