Question

Check whether the following are quadratic equations
16x²-3=(2x+5)(5x-3)

Answer 1

AnsWer :

Yes.

SolutioN :

We have, Equation.

→ 16x² - 3 = ( 2x + 5 )( 5x - 3 )

→ 16x² - 3 = 10x² - 6x + 25x - 15.

→ 16x² - 10x² = 25x - 6x - 15 + 3.

→ 6x² = 19x² - 12.

→ 6x² - 19x + 12 = 0.

$\rule{100}2$

✎ Compare With General Equation.

☛ ax² + bx + c = 0.

Where as,

• a = 6.
• b = - 19.
• c = 12.

✡ Yes, it is a Quadratic Equation.

Answer 2

Question:

Check whether the following are quadratic equations

16x²-3=(2x+5)(5x-3)

$\rule{230}2$

: General equation

$\leadsto\maltese\tt \:ax^2+bx+c\:\maltese$

:-Solution-:

$\implies\tt 16x^2-3=(2x+5)(5x-3)\\\implies\tt 16x^2-3=10x^2-6x+25x-15\\\implies\tt 16x^2-10x^2=19x-15+3\\\implies\tt 16x^2-10x^2=19x-12\\\implies\tt 6x^2-19x+12=0$

Now,

comparing with general equation

$\maltese\tt a=6\\\maltese\tt b=-19\\\maltese\tt c=-12$

So,

The given equation is QUADRATIC .