Question

i find the value of p for which the quadratic equation
has real and equal roots 2x² +p x + 9/2 = 0​

Answer 1

Question:

Find the value of p for which the quadratic equation 2x^2 + px + 9/2 = 0

has real and equal roots.

Solution:

The given quadratic equation is;

2x^2 + px + 9/2 = 0

Also;

Determinant = b^2 - 4•a•c

=> D = p^2 - 4•2•(9/2)

=> D = p^2 - 36

We know that;

For real and equal roots, the determinant of the quadratic equation must be equal to zero.

ie;

=> D = 0

=> p^2 - 36 = 0

=> p^2 = 36

=> p = ±√36

=> p = ± 6

Hence,

For real and equal roots of the given quadratic equation, p must take the values 6 or -6.