Question

find the zeros of the followning quadratic polynomials and verify the relation between the zeros and the coefficients t^2+15​

Answer 1

Step-by-step explanation:

Correct question :-

• Find the zeros of the followning quadratic polynomials and verify the relation between the zeros and the coefficients t²- 15

Solution :-

Given -

• p(t) = t² - 15

To Find -

• Zeroes of the polynomial
• Verify the relationship between the zeroes and the coefficient

Now,

→ t² - 15 = 0

By using the identity :-

(a + b)(a - b) = a² - b²

→ (t + √15)(t - √15)

Zeroes are -

→ t + √15 = 0 and t - √15 = 0

→ t = -√15 and t = √15

Verification :-

• α + β = -b/a

→ √15 + (-√15) = -(0)/1

→ 0 = 0

LHS = RHS

And

• αβ = c/a

→ √15 × -√15 = -15/1

→ -15 = -15

LHS = RHS

Hence,

Verified..

It shows that our answer is absolutely correct.

Answer 2

$\huge{\underline{\bf{\purple{Question:-}}}}$

find the zeros of the followning quadratic polynomials and verify the relation between the zeros and the coefficients t^2-15

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$\large{\underline{\bf{\green{Given:-}}}}$

✰ p(x) = t² - 15

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to find the zeroes of the given polynomial and also find the relationship between the zeroes and coefficients.

$\huge{\underline{\bf{\red{Solution:-}}}}$

$: \implies \sf$t² - (√15)²

$: \implies \sf\:(t)^2-(\sqrt{15})^2$

$: \implies \bf\:a^2-b^2=(a+b)(a-b)$

$: \implies \sf$( t +√15)(t -√15)

$: \implies \sf$t = -√15 or t =√15

Let α = √15

and β = -√15

Relationship between the zeroes and coefficients:-

α + β = - b/a

αβ = c/a

sum of zeroes:-

$: \implies \sf$√15+(- √15)= 0/1

$: \implies \sf$0 = 0

Product of zeroes:-

$: \implies \sf$√15 × (-√15) = -15/1

$: \implies \sf$ -15 = -15

LHS = RHS

Hence Relationship is varified.

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