Question

0.2. The zeroes of the polynomial x2 + x - 2are
0 2,1
O 2-1
0 2,1
0 -21​

Answer 1

Answer :

›»› The zeroes of the polynomial x² + x - 2 are -2 and 1.

o 2, 1.

o 2, -1.

o 2, 1.

◉ -2, 1.

Step-by-step explanation :

Given :

• Quadratic polynomial = x² + x - 2.

To Find :

• Zeroes of polynomial = ?

Solution :

Let us assume that, the given polynomial be denoted by f(x). Then,

→ f(x) = x² + x - 2

→ f(x) = x² + 2x - x - 2

→ f(x) = x(x + 2) - x - 2

→ f(x) = x(x + 2) - (x + 2)

→ f(x) = (x + 2) (x - 1)

∴ f(x) = 0

→ f(x) = (x + 2) (x - 1) = 0

→ f(x) = x + 2 = 0 or x - 1 = 0

→ f(x) = x = -2 or x = 1.

Hence, the zeroes of the given polynomial are -2 and 1.

So, option (d) -2, 1 is correct ✔.

Answer 2

${\bold{\sf{\underline{Understanding \: the \: concept}}}}$

This question says that there is a equation given & and we have to find the zero of the polynomial x² + x - 2 There are some options are given for that :

• 2 , 1
• 2 , -1
• 2 , 1
• -2 , 1

${\bold{\sf{\underline{Given \: that}}}}$

Equation = x² + x - 2

${\bold{\sf{\underline{To \: find}}}}$

Zero of equation ( polynomial )

${\bold{\sf{\underline{Solution}}}}$

Zero of equation ( polynomial ) = Option d that is -2 , 1

${\bold{\sf{\underline{Some \: procedure}}}}$

To solve this problem there are so many ways but let's use the way ~ By middle term splitting method. Using this method we have to split the values (Continuing....) and we get our final result very easily and it's -2 , 1

${\bold{\sf{\underline{Full \: solution}}}}$

• x² + x - 2

☃ By middle term splitting method

• x² + (2-1) x - 2

• x² + 2x - 1x - 2

• x(x-2) - 1(x-2)

• x(x+2) - 1(x+2)

• (x-1) (x+2)

❍

• ➝ (x-1) = 0

• ➝ x = 1

❍

• ➝ (x+2) = 0

• ➝ x = -2

Henceforth, x = 1 or -2 means zero of polynomial = -2 or 1