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3 years ago

What is the value of b2 - 4ac for the following equation? 5x2 + 7x = 6

Mathematics

2 answers:

Ratling [72]3 years ago

8 0

Answer:

$\text{The value of }(b^2-4ac)\thinspace is\thinspace 169$

Step-by-step explanation:

Given the equation $5x^2 + 7x = 6$

we have to find the value of $b^2-4ac$

Equation: $5x^2+7x-6=0$

Comparing above with general quadratic equation $ax^2+bx+c=0$

we get, a=5, b=7 and c=-6

$b^2-4ac=(7)^2-4(5)(-6)=49+120=169$

Hence,

$\text{The value of }(b^2-4ac)\thinspace is\thinspace 169$

shtirl [24]3 years ago

5 0

B²-4ac?

5x²+7x-6 = 0 
the form is ax²+bx+c = 0 

a=5, b=7, c=-6 

The discriminant D = b²-4ac 
= 7² - 4(5)(-6) = 49 + 120 
= 169

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For the second condition, we need to find the derivative $y'$ first. In this case, we have:

$y'(x) = \left(c_1\textrm{e}^x + c_2\textrm{e}^{-x}\right)' = c_1\textrm{e}^x - c_2\textrm{e}^{-x}.$

Therefore:

$y'(-1) = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e}^{-(-1)} = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e} = -3.$

This means that we must solve the following system of equations:

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If we add the equations above, we get:

$\left(c_1\textrm{e}^{-1} + c_2\textrm{e}\right) + \left(c_1\textrm{e}^{-1} - c_2\textrm{e} \right) = 3-3 \iff 2c_1\textrm{e}^{-1} = 0 \iff c_1 = 0.$

If we now substitute $c_1 = 0$ into either of the equations in the system, we get:

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