The roots of the quadratic equation 9x2 + 3kx + 4 = 0 are equal if

Option c: k = ± 4. Solution: Given the quadratic equation: 9x2 + 3kx + 4 = 0 Here, the coefficients are: a = 9 , b = 3k , and c = 4 . For the roots of a quadratic equation to be equal, the discriminant D must be zero ( D = 0 ): D = b2 - 4ac = 0 Substitute the coefficients into the discriminant formula: (3k)2 - 4(9)(4) = 0 9k2 - 144 = 0 9k2 = 144 k2 = 16 k = ± 4 Therefore, the roots are equal if k = ± 4 . Option c

The roots of the quadratic equation $9x^2 + 3kx + 4 = 0$ are equal if

The correct answer is Option c: $k = \pm 4$. Given the quadratic equation: $$9x^2 + 3kx + 4 = 0$$ Here, the coefficients are: $a = 9$, $b = 3k$, and $c = 4$. For the roots of a quadratic equation to be equal, the discriminant $D$ must be zero ($D = 0$): $$D = b^2 - 4ac = 0$$ Substitute the coefficients into the discriminant formula: $$(3k)^2 - 4(9)(4) = 0$$ $$9k^2 - 144 = 0$$ $$9k^2 = 144 \implies k^2 = 16 \implies k = \pm 4$$ Therefore, the roots are equal if $k = \pm 4$. **Option c**

EquationsMCQMTP Nov 20Question 1074 of 221

All Questions

The roots of the quadratic equation $\displaystyle 9x^2 + 3kx + 4 = 0$ are equal if

Options

\displaystyle k = \pm 3

\displaystyle k = \pm 2

\displaystyle k = \pm 4

\displaystyle k = \pm 5

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Correct Answer

✅ Option c — $\displaystyle k = \pm 4$

All Options:

A $\displaystyle k = \pm 3$
B $\displaystyle k = \pm 2$
C $\displaystyle k = \pm 4$
D $\displaystyle k = \pm 5$

Detailed Solution & Explanation

Given the quadratic equation:

9x^2 + 3kx + 4 = 0

Here, the coefficients are:

\displaystyle a = 9

\displaystyle b = 3k

, and

\displaystyle c = 4

.

For the roots of a quadratic equation to be equal, the discriminant

\displaystyle D

must be zero (

\displaystyle D = 0

D = b^2 - 4ac = 0

Substitute the coefficients into the discriminant formula:

(3k)^2 - 4(9)(4) = 0

9k^2 - 144 = 0

9k^2 = 144 \implies k^2 = 16 \implies k = \pm 4

Therefore, the roots are equal if

\displaystyle k = \pm 4

.

**Option c**

About This Chapter: Equations

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Linear, Quadratic and Cubic Equations

This chapter covers Linear, Quadratic and Cubic Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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The roots of the quadratic equation 9x2+3kx+4=0\displaystyle 9x^2 + 3kx + 4 = 09x2+3kx+4=0 are equal if