If a x2+b x+c=0 with real coefficients a, b, c and a ≠ 0, then I. Discriminant, D=b2-4 a c. II. For D ≥ 0, equation has real roots. III. For D

Question

If a x2+b x+c=0 with real coefficients a, b, c and a ≠ 0, then I. Discriminant, D=b2-4 a c. II. For D ≥ 0, equation has real roots. III. For D< 0, equation has imaginary roots. IV. For D< 0, x=(-b ± i √4 a c-b2/2 a). (A) I and II are correct (B) II, III and IV are correct (C) I, II and IV are correct (D) All are correct

Tardigrade Admin · Accepted Answer

If a x2+b x+c=0 is the quadratic equation, a, b and c ∈ R, a ≠ 0. Then, discriminant, D=b2-4 a c By quadratic formula, x=(-b ± √D/2 a) ∴ Root of quadratic equation will be positive, if D ≥ 0 and roots of quadratic equation will be negative, if D< 0 x=(-b ± √(b2-4 a c)/2 a) x=(-b ± i √4 a c-b2/2 a)

Q. If ax2+bx+c=0 with real coefficients a,b,c and a=0, then I. Discriminant, D=b2−4ac. II. For D≥0, equation has real roots. III. For D<0, equation has imaginary roots. IV. For D<0,x=2a−b±i4ac−b2​​.

I and II are correct

II, III and IV are correct

I, II and IV are correct

All are correct

Q. If $a x^{2} + b x + c = 0$ with real coefficients $a, b, c$ and $a \neq = 0$ , then
I. Discriminant, $D = b^{2} - 4 a c$ .
II. For $D \geq 0$ , equation has real roots.
III. For $D < 0$ , equation has imaginary roots.
IV. For $D < 0, x = \frac{- b \pm i 4 a c - b ^{2}}{2 a}$ .