Question

Prove that the qudratic equation given below has real roots
Also find its roots by using the quadratic formula
abx^2 + (b^ - ac)x - bc = 0​

Answer 1

Answer:

$\sqrt{144} \\ \sqrt{1296} \\ \sqrt{2025}$

Answer 2

Answer:

The roots are c/b and -b/a

Step-by-step explanation:

abx² + (b² - ac)x - bc = 0​

here A=ab,B=b² - ac and C=-bc

Thus B²-4AC

=(b² - ac)²-4*(ab)(-bc)

=b⁴+a²c²-2b²ac+4b²ac

=b⁴+a²c²+2b²ac

B²-4AC=(b²+ac)²

square numbers are always positive

so B²-4AC is positive

Thus the roots are real and unequal

FIND THE ROOTS

x= { -B ±√B²-4AC}/2A

={ - (b² - ac)±√( (b² + ac)² } /2*ab

x={ - (b² - ac) ± ( (b² + ac) /2*ab

Taking + sigh

x=( -b²+ac+b²+ac)/2ab

x=2ac/2ab=c/b

Taking - sigh

x=( -b²+ac-b²-ac)/2ab

x=-2b²/2ab=-b/a

Thus the roots are c/b and -b/a