Question

The least positive integral value of $p,$ for which the roots of $4x^2-3x+p=0$ are imaginary is

• A. 1
• B. 01
• C. 1.00
• D. 1.0

Answer 1

Answer: (A), (B), (C), (D)

For quadratic equation $a{x}^2+bx+c=0,a\ne 0$
Nature of roots is given by discriminant $D=b^2-4ac$ as
$\left(i\right)D>0\Rightarrow \text{Real and Distinct roots}\left(ii\right)D=0\Rightarrow \text{Real and equal roots}\left(iii\right)D<0\Rightarrow \text{Non real or imaginary roots}$

Given quadratic equation $4x^2-3x+p=0$ have non real roots
$\therefore D<0\Rightarrow (-3{)}^2-4\times 4\times p<0\Rightarrow 9-16\times p<0\Rightarrow -16\times p<-9\Rightarrow p>\frac{9}{16}=0.5625$
Hence least positive integral value of $p=1$