Find a quadratic polynomial with sum and product of its zeroes are 0 and root 5 respectively?

Question

Answer

Given, sum of zeros = 0 and product of zeros = √5.

The required quadratic polynomial is given by,
x² - (sum of zeros)x + (product of zeros)
x² - 0x + √5
x²+√5

Answer

Sum of zeros=0
product of zeros=√5,
p(x)= x^2-(sum)x+product,

=x^2-0(x)+√5=x^2+√5

Answer

Finding a Quadratic Polynomial with Sum and Product of its Zeroes

Let's start by understanding what is meant by the sum and product of the zeroes of a quadratic polynomial.

Sum and Product of Zeroes

A quadratic polynomial is of the form ax² + bx + c, where a, b, and c are constants. The zeroes of this polynomial are the values of x that make the polynomial equal to zero.

For example, the quadratic polynomial x² + 3x - 4 has zeroes -4 and 1, since when x = -4 or x = 1, the polynomial evaluates to zero.

The sum of the zeroes of a quadratic polynomial is given by the formula:

-b/a

And the product of the zeroes is given by the formula:

c/a

Using the Formulas

Now that we know the formulas for the sum and product of the zeroes of a quadratic polynomial, we can use them to find a polynomial with sum 0 and product 5.

Let's start by setting up the equations:

-b/a = 0

c/a = 5

Since the sum of the zeroes is 0, we know that the zeroes must be opposite in sign. Let's call them x and -x.

Now we can use the product formula to solve for a:

a = c/5 = 1

So our quadratic polynomial is of the form:

x² + bx + 5

Now we can use the sum formula to solve for b:

-b/1 = 0

b = 0

So our final quadratic polynomial is:

x² + 5

Conclusion

Therefore, the quadratic polynomial with sum 0 and product 5 is x² + 5.

Answer

Let zeroes of polynomial be a and b.
ATQ,
a+b=0
ab=5
Formula of quadratic polynomial,
x2-(a+b)x+ab=0
or, x2-(0)x+5=0
or, x2-0+5=0
or, x2+5=0

Answer

X^2+root5

Answer

A+b=-0/1
ab=√5
×2-0x+√5=0

Answer

We know
sum of zeros = 0
product of zeros= √5

we know a formula
x2-(sum of zeros)x+(product of zeros)
x2 -(-0)x+(√5)
x2 + √5 is a quadratic polynomial

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