Question

Find the quad. Polynomial if sum of zeros is √2 and product of zeros is -12. Also find

zeros​

Answer 1

Answer:

small steps try this.

Step-by-step explanation:

2. $x2 - sx + p$
3. $x2 - \sqrt{2} x + ( - 12)$
4. $x2 - \sqrt{2} x - 12$

Answer 2

Step-by-step explanation:

α + β = √2

αβ = -12

Quadratic polynomial:

x²- ( α + β )x + αβ

x²- √2x -12

x²- √2x -12 is the required quadratic polynomial.

To find zeroes,

x²- √2x -12 = 0

Now, factorizing the above polynomial, we get

We will factorize the polynomial by the method of splitting the middle term.

= x² -√2x-12

= x² -(3√2-2√2)x -12

= x²-3√2x+2√2x-12

Taking x common from the first two terms and 2√2 common from the last two terms, we get

= x(x-3√2) +2√2(x-3√2)

Now, taking (x-3√2) common, we get

(x-3√2)(x+2√2) = 0

(x-3√2) = 0 , (x+2√2) = 0

x = 3√2 , x = -2√2

Hence, the zeroes of the polynomial x² -√2x-12 are 3√2 and -2√2.