Question

show that the polynomial x²+2x+7 has no zeroes?​

Answer 1

Concept :

The discriminant (D) of a quadratic polynomial tells us about its zeroes, whether it has two distinct roots or only one root or imaginary roots.

If  D > 0 ; then the quadratic polynomial has two distinct real roots

If D = 0 ; then the quadratic polynomial has one real root or two equal roots

If D < 0 ; then the quadratic polynomial has no real roots.

Solution :

Hence to check the roots of  x²+2x+7 = 0 we simply need to check its Discriminant

In x²+2x+7;

a = 1 , b = 2 , c = 7

Hence D  = b² - 4ac = 2² -4(1)(7) = 4 - 28 = -24

Since -24 < 0

Hence x²+2x+7 = 0 has no real roots