Question

determine the nature of roots for the given quadratic equation 2x²+6x-5=0​

Answer 1

Answer:

not real roots

Step-by-step explanation:

Because

Express this equation in general form

-----------------

a x² + bx - c =0

here a = 2 , B= 6 , C = -5

using quadratic formula

discriminant = b² - 4ac

36 - ( - 40)

96 > 0

•°• roots are real and distinct.

=> if the discriminant would be = 0 , then this would have equal and real roots.

=> if discriminant would be <0 , then this would have unreal roots.

Answer 2

Given:-

• 2x² + 6x - 5 = 0

To determine:-

• Nature of roots

Answer:-

We can determine the nature of roots by using the discriminant of the quadratic equation, that is D = b² - 4ac

On comparing 2x² + 6x - 5 = 0, with standard form, ax² + bx + c = 0, we get,

• a = 2
• b = 6
• c = -5

So,

D = b² - 4ac

=> D = 6² - (4 * 2 * -5)

=> D = 36 + 40

=> D = 76

Nature of roots:

• D = 0 ------- Real and equal
• D > 0 and a perfect square ----- Real, unequal and rational
• D > 0 and not a perfect square ------ Real, unequal and irrational
• D < 0 ------- Unequal and imaginary

As here 76 = D > 0, but it is not a perfect square,

the roots will be real, unequal and irrational Ans