Question

find the zero of the quadtic polynomil 8xsqure minus 4​

Answer 1

Answer- The above question is from the chapter 'Polynomials'.

Let's know about quadratic polynomial first.

Quadratic polynomial- A polynomial whose highest power of variable is 2 is called a quadratic polynomial.

Examples:

1) x² + 2x + 2

2) 2x² + 4x + 1

Relationship between zeroes and coefficients of a quadratic polynomial:

Let p(x)= ax² + bx + c be any quadratic polynomial in x.

Let α and β be its zeroes.

Sum of zeroes i.e α and β= -b/a

Product of zeroes i.e αβ= c/a

Given question: Find zeroes of the quadratic polynomial 8x² - 4.

Solution: We will solve this question by factorisation method.

p(x)= 8x² - 4

Let p(x) = 0

⇒ 8x² - 4 = 0

Transposing 4 to R.H.S., we get

8x² = 4

x² = 4/8

x² = 1/2

x = ± √(1/2)

x = ± 1/√2

Rationalising,

x = ± √2/2

∴ Zeroes of p(x) = 8x² - 4 are ± √2/2.