Which of the following equations does not have a real root ?
If ad ≠ bc, then prove that the equation: (a² + b²)x² + 2(ac + bd)x + (c² + d²) = 0 has no real roots.
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Assertion(A): The roots of the quadratic equation x² + 2x + 2 = 0 are imaginary Reason(R): If discriminant D = b² – 4ac < 0 then the roots of quadratic equation ax² + bx + c = 0 are imaginary.
Assertion (A): The polynomial p(x) = x² + 4 has no real zeros. Reason (R): A quadratic polynomial ax² + bx + c has real zeros only if b² − 4ac ≥ 0.
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
