Question

p^2+27p-90=0 solve polynomial​

Answer 1

Given :-

→ p² + 27p - 90 = 0.

Answer :-

Concept applied :-

In order to find the value of p, the equation must be factorised by using the Splitting the middle term method.

To express p² + 27p - 90 in the form of Product of it's factors, we have to split the middle term into 2 divisions such that the sum results in the middle term and it's product, the end term.

→ ax² + x(a+b) + ab

→ ax² + ax + bx + ab

This is the form the LHS (Left Hand Side of the equation) is in.

The number 'a' is the coefficient of the first term. 'b' is the end term.

The product obtained by multiplying these 2 is the number on which the factors are found to split the middle term.

Solution :-

→ p² + 27p - 90

Coefficient of p is 1. Hence,

• ab = (-90)

The factors of (-90) are :-

• 1 × -90 = -90
• -2 × 45 = -90
• 30 × -3 = -90
• -45 × 2 = -90
• -30 × 3 = -90
• -1 × -90 = -90

The only pair which when added gives (+27) is [30 × -3].

By splitting the middle term,

→ p² + 30p - 3p - 90 = 0

→ p(p + 30) - 3(p + 30) = 0

→ (p - 3)(p + 30) = 0

Therefore, p can take 2 values.

Value of p :-

Value 1 :-

$\implies \sf p - 3 = 0$

$\implies \sf p = 3$

Value 2 :-

$\implies \sf p + 30 = 0$

$\implies \sf p = ( - 30)$

Verification :-

Let us verify the answer by substituting p for 3 and (-30) respectively.

RHS :-

→ p² + 27p - 90

→ (3)² + 27(3) - 90

→ 9 + 81 - 90

→ 90 - 90

→ 0

LHS :-

→ 0

LHS = RHS

RHS :-

→ p² + 27p - 90

→ (-30)² + 27(-30) - 90

→ 900 - 810 - 90

→ 900 - 900

→ 0

LHS :-

→ 0

LHS = RHS

Hence Verified.

Answer 2

Answer:

X=30 and X=-3

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Step by step solution :

STEP

1

:

Trying to factor by splitting the middle term

1.1 Factoring x2-27x-90

The first term is, x2 its coefficient is 1 .

The middle term is, -27x its coefficient is -27 .

The last term, "the constant", is -90

Step-1 : Multiply the coefficient of the first term by the constant 1 • -90 = -90

Step-2 : Find two factors of -90 whose sum equals the coefficient of the middle term, which is -27 .

-90 + 1 = -89

-45 + 2 = -43

-30 + 3 = -27 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -30 and 3

x2 - 30x + 3x - 90

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-30)

Add up the last 2 terms, pulling out common factors :

3 • (x-30)

Step-5 : Add up the four terms of step 4 :

(x+3) • (x-30)

Which is the desired factorization

Equation at the end of step

1

:

(x + 3) • (x - 30) = 0

Solving a Single Variable Equation:

2.2 Solve : x+3 = 0

Subtract 3 from both sides of the equation :

x = -3

Solving a Single Variable Equation:

2.3 Solve : x-30 = 0

Add 30 to both sides of the equation :

x = 30