Question

find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients of ___________

t^2-15​

Answer 1

Solutions :

We have, Expression.

$\tt : \implies {t}^{2} - 15$

Let's To Find Zeros.

→ t² - 15 = 0.

→ t = ±√15.

Other Methods.

$\tt \dagger \: \: \: \: \: x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

Where as,

• a= 1.
• b = 0.
• c = 15.

$\tt : \implies x = \dfrac{ - 0 \pm\sqrt{ {0}^{2} - 4 \times 1 \times 15} }{2}$

$\tt : \implies x = \dfrac{ \pm \sqrt{60} }{2}$

$\tt : \implies x = \dfrac{ \pm2 \sqrt{15} }{2}$

$\tt : \implies x = \pm \sqrt{15}$

Let's Verify.

• Let Zeros be a and b.

★ Sum of Zeros.

→ a + b = - b / a.

→ √15 - √15 = 0.

→ 0 = 0.

★ Product of Zeros.

→ a * b = c / a

→ √15 * - √15 = - 15.

→ - 15 = -15.

Verify