Question

A teacher asks three students to complete the following statement about the nature of the roots

of a quadratic equation.
If q
2
– 4pr > 0, the roots of the quadratic equation px2 + qx + r = 0 will be...
Zain answers, "always positive".
Vipul answers, "positive, if p, q, and r are positive".
Suman answers, "negative, if p, q, and r are positive".
Who answered correctly

Answer 1

Vipul answered correctly.

The nature of the roots of a quadratic equation depends on the value of the discriminant, which is given by b^2 - 4ac, where a, b, and c are coefficients in the equation ax^2 + bx + c = 0. If the discriminant is positive, the roots of the equation will be real and distinct, and their sign will depend on the sign of the coefficients a, b, and c. If p, q, and r are positive, the value of the discriminant (q^2 - 4pr) will be positive, and the roots of the equation px^2 + qx + r = 0 will be real and distinct, but their sign cannot be determined just based on the values of p, q, and r alone.

Answer 2

Vipul answered correctly.

If q^2 - 4pr > 0, the roots of the quadratic equation px^2 + qx + r = 0 will be real and distinct. Whether the roots are positive or negative depends on the values of p, q, and r. If p, q, and r are positive, then the roots can be either positive or negative, and Vipul's statement that they will be positive is correct. Zain's statement that the roots are always positive is not correct, and Suman's statement that the roots will be negative if p, q, and r are positive is also not correct.