If p and q are positive then the roots of the equation $x^2-px-q=0$ are-
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imaginary
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real & both positive
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real & both negative
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real & of opposite sign
Reveal answer
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D
Correct answer
Explanation
For x^2 - px - q = 0, the discriminant D = (-p)^2 - 4(1)(-q) = p^2 + 4q. Since p and q are positive, D > 0, so roots are real. The product of roots is -q. Since q > 0, the product is negative, meaning the roots have opposite signs.
AI explanation
The discriminant of the quadratic equation is p squared plus 4q. Since p and q are both positive, the discriminant is strictly greater than zero, meaning the roots are real. The product of the roots equals q divided by 1, which is negative, meaning the roots must have opposite signs. The result is real and of opposite sign.