How is this problem factored? 35x^2-57x-44

Mathematics

1 answer:

faust18 [17]3 years ago

7 0

You can use the quadratic formula with it which will be easier
or simple factoring
it will be (5x-11)(7x+4)

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a function is defined on the complex numbers by where and are positive numbers. this function has the property that for each com

dedylja [7]

The value of p+q = 403,For the given complex number a+bi and $b^{2} =\frac{p}{q}$

where p and q are co-primes

F(z)= (a+ib)z⇒this is equidistant from "0" and "z"

Given modulus of complex number (a+ib) = 10 ; $b^{2} =\frac{p}{q}$ p and q ∈Z

G.C.D of ( p and q)=1

(a+ib)z equidistant from "0" and "z"

$&\Rightarrow|(a+i b) z-z|=|(a+i b) \bar{z}-0|\\&|z(a+i b-1)|=|(a+i b) \bar{z}|\\&[\bar{z}||(a-1)+i b|=| z|(a+i b)|\\&|a-1+i b|=|a+i b|\\&\sqrt{(a-1)^2+b^2}=\sqrt{a^2+b^2}\\&|a+i b|=10 \quad a^2+1-2 a+b^2=x^2+b^2\\&\sqrt{a^2+b^2}=10\\&a=1 / 2\\&a^2+b^2=100\\&b^2=100-\frac{1}{4}\\$

$b^{2} =\frac{399}{4}$

p = 399 and q= 4

p+q= 399+4

p+q=403

Hence the value of p+q = 403

Complete question:A function f is defined on the complex number by f (z) = (a + bi)z, where 'a' and 'b' are positive numbers. This function has the property that the image of each point in the complex plane is equidistant from that point and the origin. Given that |a+bi|=8 and that $b^{2} =\frac{p}{q}$ where p and q are coprime. Find the value of (p+q)

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san4es73 [151]

(1+1/2+1/4) divided by

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