Five mark example problem III — task. Mathematics State Board, Class 10.

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Answer variants:

real and unequal roots

$r^{2} + s^{2}$

$4 [{(ps - qr)}^{2}] > 0$

real and equal

$p^{2} + q^{2}$

$Δ = 0$

$- 4 [{(ps - qr)}^{2}] < 0$

$b^{2} - 4 ac < 0$

$- 4 {[qr - qr]}^{2} = 0$

$4 {[qr - qr]}^{2} = 0$

no real root

$b^{2} - 4 ac > 0$

$2 (pr + qs)$

Prove that the equation

$x^2(p^2 + q^2) + 2x(pr + qs) + r^2 + s^2 = 0$ has no real roots. If

$ps = qr$ , then show that the roots are real and equal.

Answer:

Here,

$a =$

$b =$

$c =$

$\Delta = b^2 - 4ac =$

Since

$\Delta =$

, the given equation has

$ps = qr$ , then

$\Delta =$

Therefore,

$ps = qr$ and so the roots will be

Hence, we proved.

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17. Five mark example problem III