Question

zero of the polynomial 4x^3-3x^2-6x+32 is

Answer 1

Okay boy...... Let's see..
The polynomial is P(x) = 4x³ - 3x² - 6x + 32
Note: Usually, the ratio (Factors of constant term / Factors of leading co-efficient) is the zero...
So, we note the ratios....... But simply, you can use Hit and trial with the Factors of "32" in this case to get the Zero.... As, Substituting for ±1,±2,±4,etc..

And so, we get -2 is a zero.... Factorizing the Polynomial further, we have::
P(x) = (x+2)(4x² - 11x + 16)

As for the second Factor, the discriminant D of ax² + bx + c = b² - 4ac
And we know, if D<0, the roots of eqn. is not real...
So, For the second factor, b² - 4ac = 11² - 4*64 < 0

Hence, we have imaginary soln.s for the eqn. which are { (11 ± √-135) / 2 } ...

As you've asked for a zero...... Use -2 only, cause the rest are not real.... Got it.....

Further, to verify, put x=2 in P(x) and you'll get P(2) = 0

Answer 2

Answer:

your answer is -2

Step-by-step explanation:

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