Listen NCERT Audio Books to boost your productivity and retention power by 2X.
If a and b are distinct real numbers, show that the quadratic equation 2 (a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots.
Given: 2 (a2 + b2)x2 + 2(a + b)x + 1 = 0
Comparing with standard quadratic equation ax2 + bx + c = 0
a = 2 (a2 + b2), b = 2(a + b), c = 1
Discriminant D = b2 – 4ac
= [2(a + b)]2 – 4. 2 (a2 + b2).1
= 4(a2 + b2 + 2ab) – 8 a2 – 8b2
= 4a2 + 4b2 + 8ab – 8a2 – 8b2
= – 4a2 – 4b2 + 8ab
= – 4(a2 + b2 – 2ab)
= – 4(a – b)2 < 0
Hence the equation has no real roots.