Assertion(A): If the coefficient of x² and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots. Reason (R): Every quadratic equation has at least two roots.

Free previous-year papers & practice for JEE, NEET and CBSE Boards.

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Nature of Roots Based on Discriminant | PadhAiPro

Question

Assertion-ReasonNature of Roots Based on Discriminant

For the equation x² + 5x – 1, which of the following statements is correct?

Assertion (A): The quadratic equation x² + 4x + 5 = 0 has no real roots. Reason (R): The discriminant is greater than zero.

Find the discriminant of the equation 3x² – 2x + 1/3 = 0 and hence find the nature of its roots. Find them, if they are real.

The least positive value of k, for which the quadratic equation 2x² + kx – 4 = 0 has rational roots, is

Assertion (A) : The polynomial p(x) = x² + 3x + 3 has two real zeroes. Reason (R): A quadratic polynomial can have at most two real zeroes.

Find the sum and product of the roots of the quadratic equation 2x² – 9x + 4 = 0.