Question

If a and B are the roots of 2x2 – 3x - 1 = 0, then the value of a² + B2 is
(a)
13
2.
(b) =
13
4
(c)
13
4
(d) -
-13
2​

Answer 1

Given:

1) 2x²-3x-1=0........(Quadratic Equation)

2) a and B are the roots of the quadratic equation

To Find:

a²+B²=?

Solution:

2x²-3x-1=0

It is given that a and B are the roots of the given quadratic equation.

So,

Comparing the above equation with

ax²+bx+c=0..... (General form of quadratic equation)

: . a=2 , b= -3 and c= -1

Sum of the roots(a+b)=-b/a=3/2

Product of the roots(ab) =c/a=-1/2

a2+B²=(a+B) ²-2aB

a²-B²=(3/2) ²-2(-1/2)

a²-B²=9/4+2/2

a²-B²=9/4+1

a²-B²=9+4/4

a²-B²=13/4

Option B)