Question

Find the quadratic polynomial whose zeroes are -2 and -5. Verify the relationship between zeroes
and coefficients of the polynomial

Answer 1

${\bf{\underline{\underline{\underline{\red{Given \; :-}}}}}}$

Zeroes = -2 and -5

${\bf{\underline{\underline{\underline{\red{To\;find \; :-}}}}}}$

Quardatic polynomial

${\bf{\underline{\underline{\underline{\red{Solution\; :-}}}}}}$

Sum of zeroes = -2 + (-5)

Sum of zeroes = -2 - 5

Sum of zeroes = -7

Product of zeroes = -2 × -5

Product of zeroes = 10

Now

Standard form of a polynomial is given by = x² - (α + β)x + αβ

=> x² - (-7)x + 10

=> x² + 7x + 10

Now

Verifying the relationship between  zeroes  and coefficients of the polynomial

Sum of zeroes = -b/a

= -(7)/1

= -7

Product of zeroes = c/a

= 10/1

= 10

Hence, Verified

[tex][/tex]

Answer 2

Step-by-step explanation:

Question :-

Find the quadratic polynomial whose zeroes are -2 and -5. Verify the relationship between zeroes

and coefficients of the polynomial

Solution :-

Given :

• Zeros of quadratic polynomial = -2 and -5

The formula being used :

${\large{\mathfrak{\fbox{Quadratic equation = x² - (Sum of zeros)x + (Product of zeros)}}}}$

Let's do further calculations,

${\bold{\sf{: \: ⟹ \: \: \: \: \: x² \: - [(-2) \: + \: (-5)]x \: + \: [(-2) \: × \: (-5)]}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: x² \: - \: 7x \: + \: 10}}}$

Hence the quadratic equation that form is x² + 7x + 10