Question

The sum and product respectively of zeroes of the polynomial x²-7x+4 are​

Answer 1

$\underline{\bf{GIVEN:-}}$

Polynomial = x²-7x+4

$\underline{\bf{TO \: FIND:-}}$

Sum and product of zeroes of polynomial.

$\underline{\bf{SOLUTION :-}}$

By comparing the given polynomial by ax² + bx + c = 0, a=1; b=-7; c=4.

$\sf \: Sum \: of \: zeroes = \dfrac{ - b}{a} = \dfrac{ - ( - 7)}{1} = 7$

$\sf \: Product \: of \: zeroes = \dfrac{c}{a} = \dfrac{4}{1} = 4$

Therefore, sum of zeroes of polynomial is 7 and product is 4.

$\underline{\bf{More \: To \: Know:-}}$

When value of a polynomial is zero, if a polynomial is replaced by a real number in place of a variable in a polynomial, then the real number is called the zero of the polynomial.

Answer 2

Step-by-step explanation:

Given Polynomial:-

${x}^{2}-7x+4$

To do:-

Find the sum and zeros of the polynomial

Solution:-

Let

the two zeros are ${\alpha}\;,{\beta}$

by comparing with equation ${ax}^{2}+bx+c$

We get

• a=1
• b=-7
• c=4

$\sf {Sum\;of\;zeros={\alpha}+{\beta}}$

$\sf {Product\:of\;zeros={\alpha}{\beta}}$

• Now using Quadric formula we get solution

${:}\dashrightarrow$$\sf {{\alpha}+{\beta}={\dfrac {-b}{a}}}$

${:}\dashrightarrow$${\dfrac {-(-7)}{1}}$

${:}\dashrightarrow$${\dfrac {7}{1}}$

${:}\dashrightarrow$${\underline{\boxed{\bf {{\alpha}+{\beta}=7}}}}$

${:}\dashrightarrow$$\sf {{\alpha}{\beta}={\dfrac {c}{a}}}$

${:}\dashrightarrow$${\dfrac {4}{1}}$

${:}\dashrightarrow$${\underline{\boxed{\bf {{\alpha}{\beta}=4}}}}$

$\therefore$$\sf {Sum\:of\;zeros=7{\quad}and {\quad}Product\:of\;zeros=4}$