Question

The discriminant of the equation ( x+2) ( x-5) = 0 is

Answer 1

EXPLANATION.

Discriminant of the Equation = ( x + 2 ) ( x - 5 ) = 0.

Factorizes the equation, we get.

⇒ ( x + 2 ) ( x - 5 ) = 0.

⇒ x² - 5x + 2x - 10 = 0.

⇒ x² - 3x - 10 = 0.

⇒ x² - 5x + 2x - 10 = 0.

⇒ x ( x - 5 ) + 2 ( x - 5 ) = 0.

⇒ ( x + 2 ) ( x - 5 ) = 0.

⇒ x = -2 and x = 5.

Discriminant = D = b² - 4ac.

⇒ (-3)² - 4(1)(-10) = 0.

⇒ 9 + 40 = 0.

⇒ 49

D = 0 Or b² - 4ac = 0 ⇒ Roots are real and equal.

                                                           

MORE INFORMATION.

NATURE OF ROOTS.

The term b² - 4ac is called discriminant of the equation. it is denoted by Δ or D.

(A) = Suppose a , b , c ∈ R and a ≠ 0 then,

(a) = If D > 0 Roots are real and unequal.

(b) = If D = 0 Roots are real and equal and each equal to = -b/2a.

(c) = If D < 0 Roots are imaginary and unequal or complex.

(B) Suppose a , b , c ∈ Q , a ≠ 0.

(a) = If D > 0 & D is perfect square = roots are unequal & rational.

(b) = If D > 0 & D is not perfect square = roots are irrational and unequal.

Answer 2

Solution:-

We have the equation

⇒(x+2)(x-5)

⇒x²-5x+2x-10

⇒x²-3x-10

Now, comparing the above equation with ax²+bx-c , we get

a=1, b=-3 and c=-10

Now We know that D=b²-4ac

D⇒(-3)²-4×1×(-10)

D⇒9-(-40)

D⇒9+40

D⇒49

Here D>0 , thus the roots are real.

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More to know :-

• If Discriminant ,D<0 then the roots are imaginary .
• If Discriminant ,D=0 then the roots are real and equal .
• If Discriminant D>0 then the roots are real.