Question

find the nature of the roots of the following quadratic equations if real roots exist, find them x²+7x-60=0​

Answer 1

Given,

• Quadratic polynomial, x² + 7x - 60 = 0

To Find,

• The nature of the roots.

According to question,

Given, quadratic polynomial, x² + 7x - 60 = 0

On comparing with, ax² + bx + c = 0 , We get ;

⟶ a = 1 , b = 7 , c = -60

We know that,

Discriminate (Δ)

⟶ b² - 4ac

[ Put the values ]

⟶ (7)² - 4 × 1 × -60

⟶ 49 - 4 × -60

⟶ 49 + 240

⟶ 289

.°. Δ > 0

Therefore,

The roots are real and unequal.

Answer 2

Step-by-step explanation:

Now,

x² −7x−60=0

or, x²−12x+5x−60=0

or, x(x−12)+5(x−12)=0

or, (x−12)(x+5)=0

or, x=12,−5.

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