Question

find a quadratic polynomial whose zeros are 2 and -5​

Answer 1

Answer:

given zeroes are 2 and -5

their sum = 2 + ( -5) = 2 - 5 = -3

and

product of zeroes = 2*( -5) = -10

so,

required quadratic polynomial is

x² -( sum)x + product = 0

=> x² -( -3)x + ( -10) = 0

=> x² +3x - 10 = 0.

this is the required quadratic equation.

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Step-by-step explanation:

some important relations...

for a quadratic equation of the form

ax² + bx + c = 0

then,

sum of zeroes = -b/a

and product of zeroes = c/ a

Answer 2

Answer:

$x^{2} +3x-10 = 0$

Step-by-step explanation:

roots of a quadratic equations be $\alpha ,\beta$

$\alpha +\beta =\frac{-b}{a} \\\alpha \beta =\frac{c}{a}$

so lets substitute 2+(-5) in -b/a

and 2*-5 in c/a we get,

a = 1

b = 3

c = -10

therefore ,

we know that quadratic equation is in the form of $ax^{2} +bx+c = 0$

lets substitute the value of a , b and c in the equation we get,

$x^{2} +3x-10 = 0$

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