Multiple choice

Let $\displaystyle \alpha, \beta $ are roots of $\displaystyle f\left ( x \right )=3x^{2}-4x+5=0. $ The equation whose roots are $\displaystyle 2\alpha, 2\beta $ is given by $\displaystyle 3x^{2}+8x-20=0$.

  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

  2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

  3. Assertion is incorrect but Reason is correct

  4. Both Assertion and Reason are incorrect
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

To find the new equation with roots multiplied by 2, substitute x divided by 2 into the original equation 3x squared - 4x + 5 = 0. This gives 3(x/2) squared - 4(x/2) + 5 = 0, which simplifies to 3x squared divided by 4 - 2x + 5 = 0. Multiplying by 4 yields 3x squared - 8x + 20 = 0, proving the given assertion is incorrect while the transformation reason remains a valid mathematical method.

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