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Answer 1

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Answer 2

QUADRATIC EQUATION

An equation in which the highest degree of the variable is 2, is known as a quadratic equation.

The general formula for a quadratic equation is :-

ax² + bx + c = 0

where a, b and c are constants and x is the variable and a ≠ 0.

ATQ,

Given equation :- x² + ax - 4 = 0

Compare the given equation with the general quadratic equation which is ax² + bx + c = 0

After comparison :-

a = 1

b = a

c = -4

Substitute the values in the discriminant formula.

D = b² - 4ac

D = a² - (4×1× (-4))

D = a² + 16

Now, let us recall the discriminant rules :-

• If D > 0, then roots are distinct and real.
• If D = 0, then roots are same and real or only one real root exists.
• If D < 0, then roots are imaginary or roots does not exist.

By solving the discriminant of the given equation, we can clearly see that a² + 16 > 0

=> The given equation has real and distinct roots.