Question

For what value of p the quadratic equation px2+2x-3=0 can be factorized into real and linear factor. Ans:[p ≥ -1/3]

Answer 1

Step-by-step explanation:

Solution:-

for roots to be cal 'D' must be grater than equal to zero.

$\color{darkcyan}\[ \begin{array}{l} \tt \Rightarrow \quad D=b^{2}-4 a c \\ \\ \tt \Rightarrow(2)^{2}-4(p)(-3) \\ \\ \tt \Rightarrow 4+12 p \geq 0 \\ \\ \tt 12 p \geq-4 \\ \\ \tt p \geq- \dfrac{4}{12} \\ \\ \tt p \geq - \dfrac{1}{3} \end{array} \]$

Answer:- for value of $\tt \left(p \geq-\dfrac{1}{3}\right)$ the equation has real roots.