Question

find a quadrate polinomial whose zeroes are -12 and 4 and verify the relationship between the zeroes and the coefficient​

Answer 1

GIVEN:

• Zeroes of e the polynomial = –12 and 4

TO FIND:

• Find a quadratic polynomial and verify the relationship between the zeroes

SOLUTION:

Take

• $\sf{ \alpha = -12}$
• $\sf{ \beta = 4}$

We know that the sum of the zeroes is:-

$\sf{\hookrightarrow sum \: of \: zeroes = \alpha + \beta}$

$\sf{\hookrightarrow \alpha + \beta = -12 + 4 }$

$\bf{\hookrightarrow Sum \: of \: Zeroes = -8}$

Now, we have to find the product of Zeroes:

$\sf{\hookrightarrow Product \: of \: Zeroes = \alpha \times \beta }$

$\sf{\hookrightarrow \alpha \times \beta = -12 \times 4 }$

$\bf{\hookrightarrow Product \: of \: Zeroes = -48 }$

FORMATION OF POLYNOMIAL:

$\Large{\boxed{\bf{\star \: x^2 -sx + p \: \star}}}$

• s = Sum of Zeroes
• p = Product of Zeroes

On putting the values in the formula, we get

$\rm{\hookrightarrow x^2 -(-8)x + (-48) }$

$\bf{\hookrightarrow x^2 +8x -48 }$

VERIFICATION:

Sum of Zeroes = –12 + 4

• Sum of Zeroes = –8

Product of Zeroes = –12 $\times$ 4

• Product of Zeroes = –48

❍ Sum of Zeroes = –b/a

❍ Product of Zeroes = c/a

• a = 1
• b = 8
• c = –48

◈ Sum of Zeroes = –8

◈ Product of Zeroes = –48

VERIFIED.....

Answer 2

Answer:

$\huge\bold\star\red{Answer}\star$

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

Given:-

• zeroes of a quadratic polynomial which are (-12) and 4

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

To find:-

• the polynomial

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

To verify:-

• relation between zeroes and coefficient

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Solution:-

• If zeroes of a quadratic polynomial are given,we have to use the given formula to find the polynomial.

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

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

According to the formula,

we have to find ,

• sum of zeroes=?
• product of zeroes=?

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

now,

$sum\:of\:zeroes=(-12)+8$

$=(-4)$

$product\:of\:zeroes=(-12)×4$

$=(-48)$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

putting the value in the given formula,we get

${x}^{2} - ( - 4)x + ( - 48)$

$= {x}^{2} + 4x - 48$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

•°•the required polynomial is

${x}^{2} + 4x - 48$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Verification:-

sum of zeroes=(-12)+8

=(-4)

=(-4)/1

=-b/a

product of zeroes=(-12)×4

=(-48)

=(-48)/1

=c/a

Hence,verified

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

$\huge\green{hope\:this\:help\:you}$