Question

form a quadratic polynomial whose zeroes are -4 and -5
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Answer 1

$\huge\mathfrak{Answer:}$

Given:

• We have been given two zeroes of a quadratic polynomial as -4 and -5.

To Find:

• We need to find the quadratic polynomial.

Solution:

As two zeroes of quadratic polynomial are given as -4 and -5.

α = -4

β = -5

Sum of zeroes (α + β)

= -4 + (-5)

= -4 - 5

= -9

Product of zeroes (αβ)

= -4 × (-5)

= 20

Now, We can find the quadratic polynomial by this formula:

$\sf{[k( {x}^{2} - ( \alpha + \beta )x + \alpha \beta ]}$

$\implies\sf{k[{x}^{2} - ( - 9)x + 20]}$

$\implies\sf{k[{x}^{2} + 9x + 20]}$

Hence, the required polynomial is x² + 9x + 20.

Answer 2

Answer :

$\sf{Quadratic \: Polynomial = x^2 -9x + 20}$

Step-by-step explanation :

$\sf{ Given \begin{cases} Zeroes \: of \: the \: polynomial \: are \: -4 \: and -5 \end{cases}}$

We know that, when the sum and product of the zeroes of the polynomial are given then we can  make a quadratic polynomial by using the given below formula :

$\small{\implies{\boxed{\boxed{\sf{x^2 + (sum)x - product}}}}}$

Where,

• Sum of zeroes (a + b) = -4 - 5 = -9
• Product of zeroes (ab) = (-4)(-5) + 20

$\sf{\dashrightarrow Quadratic \: Polynomial = x^2 + (-9)x+ 20} \\ \\ \sf{\dashrightarrow Quadratic \: Polynomial = x^2 -9x + 20} \\ \\ \small{\implies{\boxed{\boxed{\sf{Quadratic \: Polynomial = x^2 -9x + 20}}}}}$