Question
For how many integer values of m does the equation x2−10x+(m+3)(m−4)=0 have roots of opposite signs?
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Answer:
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If the roots are of opposite signs, product of roots must be negative.
i.e.(m+3)(m−4)<0⟹−3<m<4
Number of integer values satisfying the above inequality is 6 (-2, -1, 0, 1, 2, 3).
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:
If the roots are of opposite signs, product of roots must be negative.
i.e.(m+3)(m−4)<0⟹−3<m<4
Number of integer values satisfying the above inequality is 6 (-2, -1, 0, 1, 2, 3).
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