If ad $\ne$ bc, then prove that the equation
Quadratic Equations (10)If ad $\ne$ bc, then prove that the equation
(a2 + b2)x2 + 2(ac + bd)x + (c2 + d2) = 0 has no real roots.
Answer
D = 4(ac + bd)2 - 4(a2 + b2)(c2 + d2)
= -4(a2d2 + b2c2 - 2abcd)
= -4(ad - bc)2
Since ad $\ne$ bc
Therefore D < 0
The equation has no real roots.
- Exam Year: 2017
Related Questions
- Find the roots of the quadratic equation $x^2 − x − 2 = 0 $
- A quadratic polynomial the sum and product of whose zeroes are -3 and 2 respectively, is
- Write all the values of p for which the quadratic equation $x^2 + px + 16 = 0$
- In a class test, the sum of Arun’s marks in Hindi and English is 30
- Find the nature of roots of the quadratic equation $2x^2 – 4x + 3 = 0$
- A quadratic equation whose one root is 2 and the sum of whose roots is zero, is