Question

Find e qandratic polynomial Whose Zeroes are 5 and 8

Answer 1

$\sf\huge\blue{\underline{\underline{ Question : }}}$

Find the Quadratic Polynomial whose zeroes are 5 and 8.

$\sf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

• Zeroes of a quadratic polynomial is 5 & 8.

★ To find,

• The quadratic polynomial.

★ Let,

The zeroes be :-

• $\tt\red{\alpha = 5}$
• $\tt\red{\beta = 8}$

★ Now,

$\bf\green{ :\implies Sum\:of\:the \: zeroes = \alpha + \beta }$

$\bf\:\leadsto 5 + 8$

$\bf\:\leadsto 13$

$\bf\green{:\implies Product\:of\:the\:zeroes = \alpha \beta }$

$\bf\:\leadsto 5\times 8$

$\bf\:\leadsto 40$

➡ General form of quadratic polynomial is :

$\tt\: x^{2} - (\alpha + \beta)x + (\alpha\beta) = 0$

• Substitute the zeroes.

$\bf\:\leadsto x^{2} - (13)x + 40 = 0$

$\bf\:\leadsto x^{2} - 13x + 40 = 0$

$\underline{\boxed{\rm{\purple{\therefore Quadratic \:Polynomial\:is\:x^{2} - 13x + 40 = 0}}}}\:\orange{\bigstar}$

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Answer 2

Answer:

Step-by-step explanation:

Concept:

Quadratic polynomial:

A polynomial whose highest degree monomial is of the second degree is said to be quadratic. A second-order polynomial is another name for a quadratic polynomial. Accordingly, at least one of the variables must be raised to the power of 2, and the powers of the remaining variables must be more than or equal to two but less than -1.

Multivariable quadratic polynomials are possible. The most frequently employed polynomial, however, is a univariate quadratic polynomial with a single variable. A univariate quadratic polynomial has a parabola as its graph. We will learn more about quadratic polynomials, their examples, and how to locate their roots in this post.

When a variable term in the polynomial expression has a highest power of 2, the polynomial is said to be quadratic. Only the exponent of the variable is taken into account when determining a polynomial's degree. It is not taken into account how strong a coefficient or constant term is. A quadratic equation or quadratic function is created when a quadratic polynomial is equal to 0. The roots or zeros of the quadratic equation are the name given to the solutions of such an equation.

Given:

zeroes of a quadratic polynomial are 5 and 8.

Find:

Quadratic polynomial.

Solution:

given that zeroes are 5 and 8.

let  $\alpha =5$

     $\beta =8$

Sum of the zeroes$=\alpha +\beta$

                             $=5+8$

                             $=13$

Product of the zeroes$=\alpha \beta$

                                   $=5*8$

                                   $=40$

The general form of quadratic polynomial is:

$x^2-(\alpha +\beta )x+\alpha \beta=0$

Substitute zeroes in general form of quadratic polynomial

$x^2-(\alpha +\beta )x+\alpha \beta=0$

$x^2-13x+40=0$

Hence the quadratic polynomial is

$x^2-13x+40=0$

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