Question

A quadratic polynomial with sum of zeroes -7 and product of zeroes 10 is:
1) x^2+10x+7

2) x^2+7x+10

3) x^2-10x+7

4) x^2+10x-7

​

Answer 1

Given:

• Sum of zeroes = - 7

• Product of Zeroes = 10 .

To find:

• The quadratic polymial .

Solution :

• As we know that :

• Quadratic polynomial

= x² - ( sum of Zeroes ) x + product of zeroes .

Put the given values ,

=> x² - ( -7 ) x + 10

=> x² +7x + 10 .

Hence, the x² +7x + 10 is the quadratic polynomial whose sum of Zeroes is -7 and product of zeroes is 10 .

Option 2 is correct .

Answer 2

Answer:

• Sum of Zeroes ( α + β ) = - 7
• Product of Zeroes ( αβ ) = 10
• Quadratic Polynomial = ?

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf Polynomial=x^2-(Sum\:of\:Zeroes)x+Product\:of\:Zeroes\\\\\\:\implies\sf Polynomial=x^2 -(\alpha + \beta)x + ( \alpha \beta)\\\\\\:\implies\sf Polynomial=x^2 - ( - 7)x + 10\\\\\\:\implies\underline{\boxed{\sf Polynomial=x^2 + 7x + 10}}$

⠀

$\therefore\:\underline{\textsf{Required polynomial is 2) \textbf{x ^\text2 + 7x + 10}}}.$

$\rule{180}{1.5}$

$\boxed{\begin{minipage}{5.5 cm} { \bigstar\: \textsf{For a Quadratic Polynomial :}}\\\\ {\qquad\sf p(x) = ax ^\sf2 \sf + bx + c}\\\sf with zeroes \alpha\:\sf and\:\beta \\\\\\ {\textcircled{\footnotesize1}} \:\:\alpha +\beta= \dfrac{ - \:b}{a}\:\:\bigg\lgroup\bf Sum\:of\:Zeroes\bigg\rgroup \\\\\\{\textcircled{\footnotesize2}} \: \:\alpha \beta= \sf\dfrac{c}{a}\:\:\bigg\lgroup\bf Product\:of\:Zeroes\bigg\rgroup\end{minipage}}$