Question

write the polynomial whose zeros are -3and1​

Answer 1

Answer :

The required polynomial is x² + 2x - 3

Step-by-step explanation :

Given :

The zeroes of the polynomial are -3 and 1

To find :

the polynomial

Solution :

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

⇒ Sum of zeroes = -3 + 1

    α + β = -2

⇒ Product of zeroes = (-3) (1)

    αβ = -3

The quadratic polynomial is of the form

k [ x² - (sum of zeroes)x + (product of zeroes) ]

     where k is any integer

⇒ k [ x² - (-2)x + (-3) ]

⇒ k [ x² + 2x - 3 ]

So, infinite polynomials can be formed with the given zeroes.

Put k = 1, the polynomial is x² + 2x - 3

Put k = 2, the polynomial is 2x² + 4x - 6

Thus, infinite polynomials can be formed.

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#Know more :

• Quadratic polynomial is a polynomial of degree 2.

• General form is ax² + bx + c

• We can find the zeroes by using quadratic formula,

        $\sf x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$

• b² - 4ac is called discriminant (D)

• Based on the value of discriminant, nature of roots is determined.

If D > 0 ; the roots are real and unequal

If D = 0 ; the roots are real and equal

If D < 0 ; the roots are not real i.e., complex roots

Answer 2

$\sf{Answer}$

Step by step explanation:-

Given that zeros of polynomial are -3&1

To find:-

Polynomial

Required polynomial =

x²-[sum of roots]x + product of roots

Sum of roots = -3 +1

Sum of roots = -2

Product of roots = -3×1

Product of roots = -3

So, Required polynomial is

x² -[Sum of roots]x + product of roots

x² -(-2) x -3

x² +2x -3 is the required polynomial

Veification :-

We have got equation Their roots should b equal to -3&1

x² +2x -3 =0

x² +3x -x -3 =0

x(x+3)-1(x+3)=0

(x +3)(x-1)=0

x = -3,1 hence verified