Question

Find the zeros of the quadratic polynomial and verify the relationship between the zeros and Co efficients . t²-15

Answer 1

Answer:

i) Zeroes of the polynomial = +√15 and -√15.

ii) Relationship between the zeroes and coefficient of the polynomial is verified.

Step-by-step explanation:

15 can be written as (√15)²

t²-(√15)² = (t+√15)(t-√15)

Take t+√15 = 0

t = -√15

Then, take t-√15 = 0

t = √15

Therefore √15 and -√15 are the zeroes of the polynomial.

Now, the quadratic equation that is given:

t²-0t-15

Sum of the zeroes (α+β)= -b/a = -√15+√15 = 0

= -(-0)/1

=0

Product of the zeroes (α*β) = c/a = -15/1 = -15

= -√15 * √15

=-15

Hence, the relationship is also verified.

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Answer 2

Step-by-step explanation:

t^2-15=0

t2-$\sqrt{15$]^2 = 0

[t+$\sqrt15$]    [t-$\sqrt15$]=0

t= -$\sqrt15$     t= $\sqrt15$

∝= -$\sqrt15$       β=$\sqrt15$

∝+β= -$\sqrt15$+15=0

-b/a=o

∴ ∝+β = -b/a

∝β = -$\sqrt15$*$\sqrt15$= -15

c/a= -15/1= =15

∴∝β=c/a

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