Question

when x³+5x²+ax-7 is divided by x-3, the remainder is 51 find a​

Answer 1

Answer:

a= -14/3

Step-by-step explanation:

By Remainder theorem,

f(x) = R

R=51

Let f(x)= $x^3+5x^2+ax-7$ = 51

x-3=0

=> x=3

f(3)=$3^3+5x^2+3a-7=51$

$27+5(9)+3a-7=51\\20+45=3a=51\\65+3a=51\\3a=51-65\\a=\frac{-14}{3}$

Answer 2

Answer:

a = (-14/3)

Step-by-step explanation:

We have,

p(x) = x³ + 5x² + ax - 7

We can solve it in two ways

Method 1

Now,

Let x - 3 = 0

Then,

x = 3

Using Remainder theorem, according to the Question,

p(3) = 51

Now, we know that,

p(x) = x³ + 5x² + ax - 7

Then,

p(3) = (3)³ + 5(3)² + a(3) - 7

51 = 27 + 45 + 3a - 7

51 = 3a + 65

3a = 51 - 65

3a = -14

a = -14/3

Method 2

We can simply divide p(x) and (x - 3) and equate the gotten remainder equal to 51, like the Question says,

Let's divide p(x) and (x - 3)

x² + 8x + (a + 24)

_____________

x - 3 | x³ + 5x² + ax - 7

- (x³ - 3x²)

—————

0 + 8x² + ax

- (8x² - 24x)

——————

0 + (a + 24)x - 7

- [(a + 24)x - 3a - 72]

——————————

0 + (-7 + 3a + 72)

So,

Remainder = (3a + 72 - 7)

R = (3a + 65)

But given,

Remainder = 51

Then,

3a + 65 = 51

3a = 51 - 65

3a = -14

a = (-14/3)

Hence,

a = (-14/3)

Hope it helped you and believing you understood it...All the best