Question

find quadratic polynomial was sum of zeroes -15 and product of it's zeroes is 26​

Answer 1

Answer:

given-sum of zeoes=-15

product of zeroes=26

We know that,

sum of zeroes=-b/a=-15/1

product of zeroes=c/a=26/1

therefore,a=1, b=-15, c=26

thus, the required quadratic polynomial is x^2-15x+26

Answer 2

EXPLANATION.

Quadratic polynomial whose,

Sum of zeroes of quadratic polynomial = -15.

Products of zeroes of quadratic polynomial = 26.

As we know that,

Quadratic equation = x² - (α + β)x + αβ.

Where,

α + β = Sum of zeroes of quadratic polynomial.

αβ = Product of zeroes of quadratic polynomial.

Put the values in equations, we get.

⇒ x² - (-15)x + 26 = 0.

⇒ x² + 15x + 26 = 0.

                                                                                                     

MORE INFORMATION.

Quadratic expression in two variables,

The general form of a quadratic expression in two variables x & y is,

⇒ ax² + 2hxy + by² + 2gx + 2fy + c.

The conditions that this expression may be resolved into two linear rational factor is,

$\sf \implies \triangle \left[\begin{array}{ccc}a&h&g\\h&b&f\\g&f&c\end{array}\right] = 0$

⇒ abc + 2(fgh) - af² - bg² - ch² = 0  and,

⇒ h² - ab > 0.

This expression is called discriminant of the above quadratic expression.