Question

Find the zeros of quadratic polynomial and verify the relationship b/w zeros and its coefficients
4xsquare-x+4​

Answer 1

Correct Question:

Find the zeros of the quadratic polynomial

4x² - 4x + 1 and verify the relation with the coefficients.

Note:

∆ The general form of a quadratic polynomial is given as ; p(x) = ax² + bx + c .

∆ Zeros of a polynomial p(x) are the possible values of x for which the p(x) become zero.

∆ To find the zeros of polynomial p(x) , operate on p(x) = 0.

∆ The maximum number of zeros of a polynomial is equal to its degree.

∆ A quadratic polynomial will have at most two zero , as its degree is 2 .

∆ If A and B are the zeros of the quadratic polynomial p(x) = ax² + bx + c , then ;

• Sum of zeros,(A+B) = - b/a

• Product of zeros,(A•B) = c/a

∆ If A and B are given zeros of a quadratic polynomial p(x)., then p(x) will be given as ;

p(x) = x² - (A+B)x + A•B

Solution:

Here,

The given quadratic polynomial is ;

4x² - 4x + 1

Clearly ,

Coefficient of x² = 4 (ie, a = 4)

Coefficient of x = -4 (ie, b = -4)

Constant term = 1 (ie, c = 1)

Now,

In order to find the zeros of the given quadratic polynomial, equate it to zero .

Thus,

=> 4x² - 4x + 1 = 0

=> (2x)² - 2•2x•1 + 1² = 0

=> (2x - 1)² = 0

=> x = 1/2 , 1/2

Hence,

The two zeros of the given quadratic polynomial are 1/2 and 1/2 .

Verification of the relation between the sum of zeros and coefficient:

Sum of zeros = 1/2 + 1/2 = 1

Also, - b/a = -(-4)/4 = 1

Clearly,

Sum of zeros = -b/a

Verification of the relation between the product of zeros and coefficient:

Product of zeros = (1/2)•(1/2) = 1/4

Also, c/a = 1/4

Clearly,

Product of zeros = c/a

Hence verified.