Question

If the roots of equation 3x² + 2x + (p + 2)(p – 1) = 0 are of opposite sign then which of the following cannot be the value of p?

Answer 1

Answer:

Step-by-step explanation:

The given quadratic equation is

3x^2+2x+(p+2)(p-1)=03x

2

+2x+(p+2)(p−1)=0

If the roots are\alpha, \betaα,β , the products of the roots is given by

\alpha\beta=\frac{(p+2)(p-1)}{3}αβ=

3

(p+2)(p−1)

If the roots are of opposite sign this procduct should be less than zero

Therefore,

\alpha\beta<0αβ<0

\implies (p+2)(p-1)<0⟹(p+2)(p−1)<0

\implies -2

Therefore, the value of p which is outside this range will be the answer

From the given options this value is -3−3

Hence Option (d) is correct.

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