Question

plzz give answer. ........​

Answer 1

SOLUTION:-

refer Attachment

It is convenient to make coefficients of x² as 1 and then convert the equation as the of difference of two square, so dividing the equation 5 in Q.1 and by 2 in Q.2

Note:- When equation is in the form of x² + bx + (b/2)² - (b/x)² + c = 0 that is, (x + b/2)² = (b/2)² - c.

Important concepts in quadratic equation:

(1) If α and β are roots of quadratic equation ax2 + bx + c = 0.

•°• α = [-b +- √(b² - 4ac)]/2a

and β = [b +- √(b² - 4ac)]/2a

(2)Nature of roots of quadratic equation ax2 + bx + c = 0 depends on the value of b2 - 4ac. Hence b2 - 4ac is called discriminant and is denoted by Greek letter ∆.

(3) (i) If ∆ = 0 The roots of quadratic equation are real and equal.

(ii) If ∆ > 0 then the roots of quadratic equation are real and unequal.

(iii) If ∆ < 0 then the roots of quadratic equation are not real.

(4) The quadratic equation, whose roots are a and b is

x2 - (a + b) x + ab = 0