Question:
The quadratic equation whose roots are three times the roots of the equation \( 2x^2 + 3x + 5 = 0 \), is
The quadratic equation whose roots are three times the roots of the equation \( 2x^2 + 3x + 5 = 0 \), is
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To scale roots by \(k\), substitute \(x \to x/k\) and simplify.
Updated On: May 8, 2026
- \( 2x^2 + 9x + 45 = 0 \)
- \( 2x^2 + 9x - 45 = 0 \)
- \( 5x^2 + 9x + 45 = 0 \)
- \( 2x^2 - 9x + 45 = 0 \)
- \( 2x^2 + 9x + 49 = 0 \)
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The Correct Option is A
Solution and Explanation
Concept:
If roots are multiplied by \(k\), replace \(x\) by \(x/k\).
Step 1: Given equation
\[ 2x^2 + 3x + 5 = 0 \]
Step 2: Replace \(x \to x/3\)
\[ 2\left(\frac{x}{3}\right)^2 + 3\left(\frac{x}{3}\right) + 5 = 0 \]
Step 3: Simplify
\[ 2\frac{x^2}{9} + x + 5 = 0 \] \[ \frac{2x^2}{9} + x + 5 = 0 \]
Step 4: Multiply by 9
\[ 2x^2 + 9x + 45 = 0 \]
Step 5: Final answer
\[ \boxed{2x^2 + 9x + 45 = 0} \]
Step 1: Given equation
\[ 2x^2 + 3x + 5 = 0 \]
Step 2: Replace \(x \to x/3\)
\[ 2\left(\frac{x}{3}\right)^2 + 3\left(\frac{x}{3}\right) + 5 = 0 \]
Step 3: Simplify
\[ 2\frac{x^2}{9} + x + 5 = 0 \] \[ \frac{2x^2}{9} + x + 5 = 0 \]
Step 4: Multiply by 9
\[ 2x^2 + 9x + 45 = 0 \]
Step 5: Final answer
\[ \boxed{2x^2 + 9x + 45 = 0} \]
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