Question

Please Solve Above Exercise..✌☺​

Answer 1

Answer:

2) b) 2x²+5x = (x+1)x + 1

3) p(2) = 4a+2b+c

Step-by-step explanation:

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(2)

A Quadratic Polynomial is a polynomial with degree 2.

Degree means highest power of variable in an expression.

In given question, four parts are there.

Expand each part and move every term to one side, then see, if final expression has a degree 2, then that option is quadratic.

Let's see one by one.

(a) (x+1)³ = x³ + 1³ + 3x² + 3x

               = x³ + 3x² + 3x + 1

Since, in this expression, degree is 3,

so, it's a cubic polynomial.

Hence, It's NOT a quadratic polynomial.

(b) 2x²+5x = (x+1)x + 1

=> 2x² + 5x = x² + x + 1

=> 2x² - x² + 5x - x - 1 = 0

=> x² + 4x - 1 = 0

Since, in this equation, degree is 3,

Hence, It's a quadratic equation.

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

=> x²-2x+x-2 = x²-x+3x-3

=> x²-x-2 = x²+2x-3

=> x²-x²-x-2x-2+3 = 0

=> -3x+1 = 0

Since, in this equation, degree is 1,

So, it's a Linear polynomial.

Hence, It's NOT a quadratic polynomial.

(d) x²+3x+1 = (x-2)²

=> x²+3x+1 = x²-4x+4

=> x²-x²+3x+4x+1-4 = 0

=> 7x-3 = 0

Since, in this equation, degree is 1,

So, it's a Linear Polynomial.

Hence, It's NOT a Quadratic Polynomial.

(3)

p(x) = ax²+bx+c

For finding p(2) just put 2 in place of x in p(x) and elaborate,

you will get your answer.

So,

p(2) = a(2)²+b(2)+c

=>p(2) = 4a+2b+c

100% CORRECT ✔️✔️

HOPE IT HELPS YOU,

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