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
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