Question

find the zeros of the following polynomial and verify the relationship between the zeros and their coefficients. ​

Answer 1

Answer:

Step-by-step explanation:

t^2 - 15

= t^2 - (√15)^2  [ a^2 - b^2 = (a+b) (a-b)

(t - √15) (t + √15)

t= √15 ; t = - √15

Relationship between zeros and their co efficient:

Sum of roots = -b/a=  0/ 1 = 0

Product of roots= c/a = -15/1 = -15

...................................................................................

Sum of roots= √15 + (-√15) = 0

Product of roots= √15 * (-√15) = -15

Hope it helps...

Answer 2

Answer:

$t^{2} -15=0$

General equation is $ax^{2} +bx+c=0$

So, compairing, a = 1, b = 0 and c = -15

Let α and β are the roots of the given equation

So, $t^{2} =15$

⇒$t=\pm \sqrt{15}$

i.e., α = $\alpha = \sqrt{15}  \text { and ]} \beta =-\sqrt{15}$

Now, $\alpha + \beta = \sqrt{15} + (-\sqrt{15}) = 0 = \cfrac{-b}{a}$

and, $\alpha\beta=(\sqrt{15})(-\sqrt{15}) = -15 = \cfrac{c}{a}$

Thus, roots are $\sqrt{15} \text { and } -\sqrt{15}$

Step-by-step explanation: