Question

3. Write a quadratic polynomial, sum of whose zeroes is 213 and product is 5.
4. Write the zeroes of the polynomial x+2x+1​

Answer 1

Answer:

$let \: a \: and \: b \: be \: the \: root \: of \: quadratic \: polynomial \: where \\ (a + b) = 213 \\ ab = 5 \\ \\ form \: of \: quadratic \: polynomial \: \\ x ^{2} + (a + b)x - (ab) \\ x ^{2} + 213x - 5$

2) x^2 + 2x +1

X^2 +x + X +1

X ( x +1) + (x +1)

(x +1) ( X +)

X = -1 , X= -1

Answer 2

QUESTION:

3. Write a quadratic polynomial, sum of whose zeroes is 213 and product is 5.

4. Write the zeroes of the polynomial x2+2x+1 (correct question )

ANSWER:

We know that. quadratic equations is in the form of

$a {x}^{2} + bx + c = 0$

where;

b = sum of zeroes

c = product of zeroes

so, in other form we can write the equation as

$\red{a {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes}$

given :

Sum of zeroes = 213

product of zeroes = 5

putting the value in the equation;

${x}^{2} - 213x + 5$

quadratic equation is;

$\huge\red{ {x}^{2} - 213x + 5}$

2ND ANSWER :

${x}^{2} + 2x + 1$

we have to factorised it to find the zeroes.

STEP 1 :

Split the middle term in such a way that it's sum equal to b i.e. 2 and product equal to a ×c that is 1

${x}^{2} + x + x + 1$

STEP 2 :

TAKING COMMON FACTOR

$x(x + 1) + 1(x + 1)$

$red{(x + 1)(x + 1) \: are \: the \: zeroes}$

so,

$x + 1 = 0 \\ x = - 1$

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