Question

Find zeros of quad. polynomial and find the relationship btw zeros and coefficients....
y^2 - 15
thanks helps me a lot to study

Answer 1

Step-by-step explanation:

Given :-

y²-15

To find :-

Find the zeroes of the quadratic polynomial and the find the relationship between zeroes and the coefficients ?

Solution :-

Given Quadratic Polynomial = y²-15

Finding the zeroes :-

Let P(y) = y²-15

=> P(y) = y²-(√15)²

It is in the form of a²-b²

Where , a = y and b = √15

We know that

(a+b)(a-b)=a²-b²

=> P(y) = (y+√15)(y-√15)

To get zeroes of P(y) ,equate it to zero

=> P(y) = 0

=> (y+√15)(y-√15) = 0

=> y+√15 = 0 or y-√15 = 0

=> y = -√15 and y = √15

The zeroes of P(y) = √15 and -√15

Let α = √15 and β = -√15

Finding the relationship between the zeroes and the coefficients:-

P(y) = y²-15

On Comparing this with the standard quadratic Polynomial ay²+by+c

a = 1

b = 0

c = -15

Sum of the zeroes = α + β

=> √15+(-√15)

=> √15-√15

=>α + β = 0---------(1)

Sum of the zeroes = -b/a

=> -0/1

=>-b/a = 0 ----------(2)

From (1)&(2)

α + β = -b/a

Product of the zeroes = α β

=> (√15)(-√15)

=> -√(15×15)

=> -(√15)²

=> α β= -15----------(3)

Product of the zeroes = c/a

=>α β = -15/1

=> α β = -15 ---------(4)

From (3)&(4)

α β = c/a

Verified the given relations in the given problem.

Answer :-

The zeroes of the given quadratic polynomial are √15 and -√15

Verified the relationship between the zeroes and the coefficients of the given Polynomial.

Used formulae:-

• The standard quadratic Polynomial in variable y is ay²+by+c

• Sum of the zeroes = -b/a

• Product of the zeroes = c/a

• (a+b)(a-b)=a²-b²