Question

check whether the following equation the quadratic or not (I) x2-6x+4=0 (ii) x3-6x2+2x-1=0 (III) x2-1/2=2 (iv) (2x+1) (3x+1)=(x-1) (x-2)​

Answer 1

$\sf\huge {\underline{\underline{{Solution}}}}$

General form of quadratic equation: ax²+bx+c

(i) x²-6x+4 = 0

It is a quadratic equation as it is in the form of ax²+bx+c which is the general form of a quadratic equation.

(ii) x³-6x²+2x-1=0

It is not satisfies the condition of quadratic equation as the highest power is 3.

Hence,it is not a quadratic equation.

(iii) x²-1/2=2

It is also not a quadratic equation as the term x is Missing here.

(iv) (2x+1)(3x+1)=(x-1)(x-2)

=> 2x(3x+1)+1(3x+1)= x(x-2)-1(x-2)

=> 6x²+2x+3x+1= x²-2x-x+2

Make like terms together

=> 6x²-x²+2x+3x+2x+x+1-2

=> 5x²+8x-1

The resultant polynomial is a quadratic equation .

More information=>

A quadratic equation is a a Equation in which the highest degree is 2 .

Form of quadratic equation : ax²+bx+c

where a,b& c ∈ R and c ≠ 0.

Answer 2

$\bf \huge \underline {\underline{✤ Solution}}$

➳ General form of quadratic equation: ax²+bx+c

$\orange{\textsf{(i) x²-6x+4 = 0}}$

☞ It is a quadratic equation as it is in the form of ax²+bx+c which is the general form of a quadratic equation.

$\orange{\textsf{(ii) x³-6x²+2x-1=0}}$

☞ It is not satisfies the condition of quadratic equation as the highest power is 3.

Hence,it is not a quadratic equation.

$\orange{\textsf{(iii) x²-1/2=2}}$

☞ It is also not a quadratic equation as the term x is Missing here.

$\orange{\textsf{ (iv) (2x+1)(3x+1)=(x-1)(x-2) }}$

$\blue{\textsf{➳ 2x(3x+1)+1(3x+1)= x(x-2)-1(x-2)}}$

$\blue{\textsf{➳ 6x²+2x+3x+1= x²-2x-x+2}}$

$\large\green{\textsf{✤ Make like terms together}}$

$\red{\textsf{➳ 6x²-x²+2x+3x+2x+x+1-2}}$

$\red{\textsf{➳ 5x²+8x-1}}$

The resultant polynomial is a quadratic equation .

More information=>

A quadratic equation is a a Equation in which the highest degree is 2 .

Form of quadratic equation : ax²+bx+c

where a,b& c ∈ R and c ≠ 0.

$\huge{\fcolorbox{cyan}{black}{\pink{Hope It Helps U :)}}}$

$\huge{\textsf{➼ MissJ0Y}}$