Question

Find the zeroes of y2 -15 and verify the relationship between the zeroes and coefficient

Answer 1

Answer: It is verified.

Given: Quadratic polynomial $y^2 -15$

To Find: Verify the relationship between the zeroes and coefficient.

Step-by-step explanation:

Step 1: For any quadratic equation $ax^2 + bx + c = 0$, the sum of the roots, α + β = -b/a. the product of the roots, α × β = c/a. Zeros can be find if we put the factor of quadratic equation equal to zero. Zeros and root both are same.

Step 2: Let $P(y)=y^2-15$

To find out zeros put P(y) = 0.

$\implies (y-\sqrt15)(y+\sqrt15)=0\\\\\implies y=\sqrt {15}, -\sqrt15$

So, the zeros of polynomial are $\sqrt15, -\sqrt15$. Now let α and β are the root of the equation. We are going to find out summation and multiplication of root and compare it to summation and multiplication of zeros.

Step 3: Now, sum of roots = $\frac{-b}{a}=\frac{0}{1}=0$

Which is also equal to sum of zeros.

Now, multiplication of roots = $\frac{c}{a} =\frac{-15}{1} =-15$

Which is also equal to product of zeros.

Hence, it is verified.

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