Question

find p (0) for the expression p(X) = (x-1) (x-2)​

Answer 1

Answer:

x=0

p(0)=(0-1)(0-2)

p(0)= -1×-2

p(0)0= 3

Answer 2

Given

The expression p(X) = (x-1) (x-2)

To Find

P(0) or the root of the equation is 0

Concept used

Directly put the x=0

Middle term splitting

Solution

It we put 0 in the equation

Then

$\rm \: (x - 1)(x - 2) = p(0)\\ \\ \rm \:(0 - 1)(0 - 2) = p(0) \\ \\ \rm{ \implies - 1 \times - 2 = p(0)} \\ \\ \: \rm \: p(0) = 2$

Method2

Now we put p(x)=0

$\rm \: (x - 1)(x - 2) = 0 \\ \\ \implies \rm \: x - 1 = 0 \: or \: x - 2 = 0 \\ \\ \implies \rm \: x = 1 \: or \: 2$

Here we found 2 roots

So we take

$\rm \: \alpha = 1 \\ \rm \: \beta = 2$

Verification

Equation

$\rm {x}^{2} - 2x - x + 2 = 0 \\ \\ \implies \rm \: {x}^{2} - 3x + 2 = 0$

We know that

$\rm \: \alpha + \beta = \dfrac{ - b}{a} \\ \\ \implies \rm \: 1 + 2 = \frac{3}{1} \\ \\ \implies \rm \: 3 = 3$

LHS=RHS

and also

$\rm \: \alpha \beta = \dfrac{c}{a} \\ \\ \implies \rm \: 2 \times 1 = \frac{2}{1} \\ \\ \implies \rm \: 2 = 2$

LHS=RHS

Hence,proved