Question

Which equation is quadratic in form?

6(x + 2)2 + 8x + 2 + 1 = 0
6x4 + 7x2 – 3 = 0
5x6 + x4 + 12 = 0
x9 + x3 – 10 = 0

Answer 1

A quadratic equation is a polynomial with an order of two. Its general form is ax² + bx + c = 0. From the choices given, the first option seems to be the quadratic equation. Simplifying the equation gives 6x² + 18x + 27 = 0. 

Answer 2

Option A is correct

Explanation:

We have been given four equations and we need to tell which one of them is quadratic

Case1:

`6(x+2)^2+8(x+2)+1`

In this we will use the formula
`(a+b)^2=a^2+b^2+2ab`

Here, a=x and b=2

The equation will become
`6(x^2+2^2+4x)+8x+16+1`

Hence, after simplification equation will become

`6x^2+24+24x+8x+16+1`

`6x^2+32x+41` which is a quadratic equation because quadratic equation is the equation is the equation which has degree 2.

In this equation degree is 2 hence, quadratic

Case2:

`6x^4+7x^2-3` is not quadratic since, degree in this equation is 4 not 2

Hence, biquadratic not quadratic

Case3:

`5x^6+x^4+12` is not a quadratic equation since, degree in this equation is 6.

Hence, not quadratic

Case4:

`x^9+x^3-10` is not quadratic since, degree in this equation is 9

Hence, not quadratic

Therefore, Option A is correct