The Dropped Factor

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PolynomialsVideo challenge · POLY01

The Dropped Factor

CBSE Class 10 · Solve it one decision at a time. A wrong pick earns a nudge, never the answer.

Step 1 of 4

The problem

The zeroes of p(x)=2x2−6x+3p(x) = 2x^2 - 6x + 3 are α\alpha and β\beta. A student calculates α2β+β2α\dfrac{\alpha^2}{\beta} + \dfrac{\beta^2}{\alpha} and gets 1515 using four lines of working:

Line 1: α2β+β2α=α3+β3αβ\dfrac{\alpha^2}{\beta} + \dfrac{\beta^2}{\alpha} = \dfrac{\alpha^3 + \beta^3}{\alpha\beta}
Line 2: α+β=3\alpha + \beta = 3 and αβ=32\alpha\beta = \dfrac{3}{2}
Line 3: α3+β3=(α+β)3−3αβ=452\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha\beta = \dfrac{45}{2}
Line 4: Answer=452÷32=15\text{Answer} = \dfrac{45}{2} \div \dfrac{3}{2} = 15

Which line contains the mistake, and what is the correct value?

Step 1 · Your move

Which line of the student’s working contains the mistake?

α2β+β2α=α3+β3αβ\dfrac{\alpha^2}{\beta} + \dfrac{\beta^2}{\alpha} = \dfrac{\alpha^3 + \beta^3}{\alpha\beta}
Helpful?