Question

A quadratic polynomial with sum and product of its zeroes as 7 and -6 is

Answer 1

$\large\bf\underline{Given:-}$

• Sum of zeroes = 7
• Product of zeroes = -6

$\large\bf\underline {To \: find:-}$

• Quadratic polynomial

$\huge\bf\underline{Solution:-}$

➛ Sum of zeroes = 7

➛ product of zeroes = -6

Let α and β are the zeroes of the required polynomial.

• ➛ α + β = 7
• ➛ αβ = -6

Formula for quadratic polynomial:-

$\bf \: {x}^{2} - ( \alpha + \beta )x + \alpha \beta$

The quadratic polynomial is :-

➸ x² -( 7)x + (-6)

➸ x² - 7x - 6

So, the quadratic polynomial is x² - 7x - 6

$\bf \underline{Verification : - }$

p(x) = x² -7x -6

• a = 1
• b = -7
• c = -6

➛ sum of zeroes = -b/a

➸ 7 = -(-7)/1

➸ 7 = 7

➛ Product of zeroes = c/a

➸ -6 = -6/1

➸ -6 = -6

LHS = RHS

Hence Verified

Answer 2

Solution:

Given that,

sum of zeroes = 7

Product of zeroes = - 6

To find,

Product of zeroes = ?

We know that

Quadratic polynomial : x² - (α + β)x + αβ

Where

• α + β : Sum of zeroes = 7
• αβ : product of zeroes = - 6

Substituting the values we have

→ x² - ( 7 )x + ( - 6)

→ x² - 7x - 6

Hence, quadratic polynomial = x²- 7x - 6

Knowledge enhancer :-

♦ Quadratic polynomial : x² - ( sum of zeroes )x + product of zeroes

♦ Quadratic formula : - b ± √b² - 4ac/2a

Where

• b : coefficient of x
• a : coefficient of x²
• c : constant term