Question

Find sum and product of the zeros of the polynomial 4x ^2 - 7x+3

Answer 1

Answer:

first multiply coefficient of x with the constant value 3×4= 12

next u need to find two numbers when u add it should give -7 and when you multiply it should give +12

so consider -4&-3 since(-4+(-3)=-7) and (-4×(-3)=12)

f(x)= 4x²-4x-3x+3

= 4x(x-1) -3(x-1)

so the roots are (4x-1)&(x-1)

equating to zero 4x-1= 0 => x= 1/4, x-1=0 => x=1

Answer 2

The sum and product of zeros of the given polynomial are 7/4 and 3/4 respectively.

Given:

A polynomial p(x) = 4x²-7x+3.

To Find:

The sum and product of zeros of the given polynomial.

Solution:

A quadratic polynomial Is a function with the highest degree 2 and having one or more variables.

Zeros of a polynomial are the values of the variable for which the value of the polynomial becomes zero. A polynomial of 'n' degree has 'n' roots or zeros. So a quadratic equation will have two zeros/roots.

The given quadratic equation is:

p(x) = 4x²-7x+3

where,

The coefficient of x² = 4

The coefficient of x = -7

The constant term = 3

For a quadratic polynomial,

Sum of zeros = $\frac{- coefficient &\ of &\ x}{coefficient &\ of &\ x^{2} }$

⇒ Sum of zeros = -(-7)/4 = 7/4

Product of zeros = $\frac{constant &\ term }{coefficient &\ of &\ x^{2} }$

⇒ Product of zeros = 3/4.

∴ The sum and product of zeros of the given polynomial are 7/4 and 3/4 respectively.

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