Answer:
See explanation.
Step-by-step explanation:
Let BC be the diameter of the circle with center at point O, AB be the chord and ∠ABC=30°. OD is the distance from the center to the chord.
Consider triangle BDO. This triangle is special 30°-60°-90° right triangle. The leg OD is opposite to the angle of 30° and is half of the hypotenuse. The hypotenuse of the triangle BDO is BO. BO is the radius of the circle and is equal to half of the diameter AB. Thus,
All triangles have a total of 180° in them.
So to find x, simply take 50° and 100° from 180°:
x = 180 - 100 - 50
= 30°
So x = 30°, and thus option D
Answer:
see first of all it is a quadratic polynomial so it will have 2 zero alpha and beta
now , we will find value of a , b, c
so,
a= 3
b= 5
c= -2
now, sum of the zeros ( alpha + beta) =-b/a
so,-5/3
now product of zeros (alpha *beta) = c/a
so, it will we -2/3
hope you get it !
<h2>
Answer:</h2>
The possible formula for a fourth degree polynomial g is:
<h2>
Step-by-step explanation:</h2>
We know that if a polynomial has zeros as a,b,c and d then the possible polynomial form is given by:
Here the polynomial g has a double zero at -2, g(4) = 0, g(3) = 0.
This means that the polynomial g(x) is given by:
![g(x)=m(x-(-2))^2(x-4)(x-3)\\\\i.e.\\\\g(x)=m(x+2)^2(x-4)(x-3)\\\\i.e.\\\\g(x)=m(x^2+2^2+2\times 2\times x)(x(x-3)-4(x-3))\\\\i.e.\\\\g(x)=m(x^2+4+4x)(x^2-3x-4x+12)\\\\i.e.\\\\g(x)=m(x^2+4+4x)(x^2-7x+12)\\\\i.e.\\\\g(x)=m[x^2(x^2-7x+12)+4(x^2-7x+12)+4x(x^2-7x+12)]\\\\i.e.\\\\g(x)=m[x^4-7x^3+12x^2+4x^2-28x+48+4x^3-28x^2+48x]\\\\i.e.\\\\g(x)=m[x^4-7x^3+4x^3+12x^2+4x^2-28x^2-28x+48x+48]\\\\i.e.\\\\g(x)=m[x^4-3x^3-12x^2+20x+48]](https://tex.z-dn.net/?f=g%28x%29%3Dm%28x-%28-2%29%29%5E2%28x-4%29%28x-3%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%28x%2B2%29%5E2%28x-4%29%28x-3%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%28x%5E2%2B2%5E2%2B2%5Ctimes%202%5Ctimes%20x%29%28x%28x-3%29-4%28x-3%29%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%28x%5E2%2B4%2B4x%29%28x%5E2-3x-4x%2B12%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%28x%5E2%2B4%2B4x%29%28x%5E2-7x%2B12%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%5Bx%5E2%28x%5E2-7x%2B12%29%2B4%28x%5E2-7x%2B12%29%2B4x%28x%5E2-7x%2B12%29%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%5Bx%5E4-7x%5E3%2B12x%5E2%2B4x%5E2-28x%2B48%2B4x%5E3-28x%5E2%2B48x%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%5Bx%5E4-7x%5E3%2B4x%5E3%2B12x%5E2%2B4x%5E2-28x%5E2-28x%2B48x%2B48%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%5Bx%5E4-3x%5E3-12x%5E2%2B20x%2B48%5D)
Also,
i.e.
Hence, the polynomial g(x) is given by:
