Question: Find the rational zeros of P(x) = x⁴ - 2x³ - 2x ² + 30x - 27.

A ) x = 1, - 3, 2 ±i5
B ) x = 1, 3, 2 ±10
C ) x = 1, 3, 2
D ) x = 1, 3, 2 + 10

Steps to derive

1 P(x) = x⁴ - 2x³ - 2x ² + 30x - 27

2 Possible rational zeros: ± 1, ± 3, ± 9, ± 27
 [By the rational zeros theorem.]





5 x² - 4x + 9 = 0
 [Solve for the depressed equation.]

6 x = -(-4)±(-4)2 - 4(1)(9)2(1)
 [Use quadratic formula.]

7 x = (4) ±(16) - 362

8 x = 2 ± i5
 [Simplify.]

9 So, the zeros of function are 1, - 3, 2 ±i5.



Hence the right answer is Option A

Click Here To Go Back


Explore Related Questions

Solve the system of equations using Gaussian elimination method. x = 10 - 3zy = 4 - 2x4z =..

Solve the system of equations by using augmented matrices. x + 1 / 2y = 203x + z = 60..

Solve the system of equations by using augmented matrices.w - y - 3z = 22w + x + y + z = 3..

Solve the system of equations by using augmented matrices. w + x - y - z = 0x + 2y + z = 4..

Find the rational zeros of P(x) = x3 - 7x - 6...

Find the rational zeros of P(x) = x3 - 13x + 12...

Find the rational zeros of P(x) = x 3 + 9x2 + 23x + 15...

Find the rational zeros of P(x) = x 3 - 5x2 - 2x + 24...

Find the rational zeros of P(x) = x 3 + 6x2 + 3x - 10...

Find the rational zeros of P(x) = x 3 + 11x2 + 38x + 40...

Find the rational zeros of P(x) = x4 + 10x 3 + 35x2 + 50x + 24...

Find the rational zeros of P(x) = x4 + 3x 3 - 24x2 - 28x + 48...

Find the rational zeros of P(a) = a3 - 2a2 - 19a + 20...

Find the rational zeros of P(a) = a4 + a3 - 39a 2 - 109a - 70...

Find the rational zeros of P(x) = x4 - 5x3 - 13x 2 + 53x + 60...

Find the rational zeros of P(x) = x3 - 3x2 - 22x + 24...

Find the zeros of the function P(x) = x3 + 6x 2 - 9x - 14...

Find the rational zeros of P(x) = x4 - 9x3 + x 2 + 81x + 70...

Find the rational zeros of P(y) = y4 - 13y3 + 56y 2 - 92y + 48..

Find the rational zeros of P(x) = 18x3 + 9x 2 - 5x - 2...

Find the rational zeros of P(x) = 12x3 + 28x 2 + 17x + 3...

Find the rational zeros of P(x) = x4 + 3x3 + 3x 2 + 3x + 2...

Find the rational zeros of P(x) = x4 + 4x3 + 12x 2 + 36x + 27...

Find the rational zeros of P(x) = x4 + 4x3 + 8x2 + 20x + 15...

Find the rational zeros of P(x) = x4 - x3 + 7x2 + 15x - 22...

Find the rational zeros of P(x) = x3 - 8x2 + 27x - 30...

Find the rational zeros of P(x) = x5 + 4x4 + 7x3 + 18x2 + 6x - 36...

Find the rational zeros of P(x) = 2x3 - 9x2 + 3x + 14..

Determine the maximum number of positive and negative real solutions of the equation P(x) ..

Determine the maximum number of positive and negative real solutions of the equation P(x) ..

Find three consecutive integers whose product is 120...

Find three consecutive odd integers whose product is 15...

What is the reciprocal of 4x + 4?..

Find the reciprocal of 14x - 6...

What is the reciprocal of 3x6x3 + 3 ?..

Multiply: 9x2y4.y945x6..

Simplify: (25x - 20)(192x + 160) · (48x + 40)(100x&nb..

Simplify: 10a2x57b2y4 ÷ 30a2x621b2y2..

Simplify: 2x2x2 + 8x + 16 ÷ 3xx2 - 16..

Simplify: (3z²+19z+20)(3z²+  10z+8) ÷ (z³ +125)(z&sup..

Evaluate: (8y + 32)(y3 - 125).(y2 -25)(y2 - 16)..

Simplify: 3y2- 12y + 3 ÷ 3y - 6(y + 3)2..

Simplify: x²+16x+48x²-3x-28 ÷ x²+24x+144x²+5x-84..

Simplify: 7t²-2t7t²-12t-4.49t²-42t-t² ÷ (7t-2)²7t-14..

Simplify: lx+ly-mx-mylx-ly+mx-my ÷ lx-ly-mx+mylx+ly+mx+my..

Simplify: [z + 3z² + 3z - 18.z² + 9z&nbs..

The expression 1y2+1 ÷ y2(1y2+1) is always positive. True or false?..

Simplify: 17l²m2l + 29lm²2l + 2..

Simplify: (5cn)2-95cn+3..

Determine whether the value of the given expression is always an even integer: (2b6)2 ..