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 value of p, for which one root of the quadratic equation $px^2 - 14x + 8 = 0$ is 6 times the other
- A plane left 30 minutes late than its scheduled time and in order to reach the destination
- Solve for x: $\frac{1}{x+1} +\frac{3}{5x+1} = \frac{5}{x+4}, x\ne-1, -\frac{1}{5}, -4$
- A quadratic equation whose one root is 2 and the sum of whose roots is zero, is
- If x = 3 is one root of the quadratic equation
- Find the roots of the quadratic equation $x^2 − x − 2 = 0 $