Find a quadratic polynomial whose zeroes are -1 and 3. Verify the relation between the coefficient and zeroes of the polynomial.
By BYJU'S Exam Prep
Updated on: October 17th, 2023
The quadratic polynomial whose zeroes are -1 and 3 is x2 + 2x − 3. The coefficients of the variables in a quadratic polynomial are directly related to the sum and product of zeros. Then, even when the zero values of a polynomial are unknown, the sum and product of zeros may be determined rather easily. The polynomial’s zeros are the values of the variable for which the polynomial as a whole has a value of 0.
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Quadratic Polynomial whose Zeroes are -1 and 3
The question states Find a quadratic polynomial whose zeroes are -1 and 3. Verify the relation between the coefficient and zeroes of the polynomial.” Any polynomial may be solved with ease using basic algebraic concepts and factorization techniques. The first step in resolving the polynomial equation is to set the right-hand side equal to 0. A polynomial solution can be explained in one of two ways:
- Solving Linear Polynomials
- Solving Quadratic Polynomials
The steps to find a quadratic polynomial, the sum and the product whose zeroes are -1 and 3 are as follows:
Let the zeroes of the quadratic polynomial be α = 1 and β = -3
Sum of zeros = α+β = -2
Product of zeros = αβ = -3
The quadratic polynomial whose product and the sum of zeroes are specified is defined as follows:
x2 – (α + β)x + αβ
x2−(−2)x+(−3)
x2 + 2x −3
Now, for verification,
Sum of zeros = -Coefficient of x/Coefficient of x2 = -2/1 = -2
Product of zeros = Constant term/Coefficient of x2 = -3/1 = -3
Hence, the relationship between the zeroes and the coefficients is verified.
Summary:
Find a quadratic polynomial whose zeroes are -1 and 3. Verify the relation between the coefficient and zeroes of the polynomial.
The quadratic polynomial whose zeroes are -1 and 3 is x2+2x−3. Division, subtraction, multiplication, and addition are polynomial operations. Any polynomial can be easily solved using fundamental algebraic ideas and factorization strategies. Setting the right-hand side of the polynomial equation equal to zero is the first step in solving it.
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