Find the solution set 7x^2-9x-10=0

Mathematics

2 answers:

Novay_Z [31]3 years ago

7 0

Answer:

x = -5/7 or x = 2

Step-by-step explanation:

7x² - 9x - 10 = 0

Factor the left side of the equation.

(7x + 5) (x - 2) = 0

Set the factors equal to 0.

7x + 5 =0

7x = -5

x = -5/7

x - 2 = 0

x = 2

vitfil [10]3 years ago

5 0

Answer:

x = -5/7, 2

Step-by-step explanation:

Step 1: Factor

(5x + 7)(x - 2) = 0

Step 2: Find <em>x </em>roots

5x + 7 = 0

x = -5/7

x - 2 = 0

x = 2

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If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate $x^4$ .

We have

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h$

Expand the numerator using the binomial theorem, then simplify and compute the limit.

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}$

In general, the derivative of a power function $f(x) = x^n$ is $\frac{df}{dx} = nx^{n-1}$ . (This is the aptly-named "power rule" for differentiation.)