Question

Find the value of p and q for which x =3/4 and x= -2 are the roots of the equation px(x)+qx-6=0

Answer 1

Answer:

p =4 & q =5

Step-by-step explanation:

$px^2 + qx - 6 = 0\\Putting values of x = \frac{3}{4}\\p(\frac{3}{4})^2 + q\frac{3}{4} - 6 = 0\\\\p(\frac{9}{16}) + q\frac{3}{4} - 6 = 0\\\\multiplying by 16\\9p + 12q - 96 = 0$

3p + 4q = 32  - Eq 1

Now Putting values of x = -2

p(-2)² + q(-2) - 6 = 0

4p -2q - 6 = 0

8p - 4q = 12  eq 2 ( multiplying by 2)    

Adding eq 1 & Eq 2

11p = 44

p = 4

putting value of p in eq 1

3×4  + 4q = 32

4q = 20

q = 5