Hey guys!❤️If you can answer this question with all the steps and working out, I'll mark your answer as the brainliest (and I'll love u 4ever)!!!
Answers
2, 5/2 ,3
Step-by-step explanation:
Given polynomial is 2x³-15x²+37x-30 =0
Zeros of polynomials are : a-b, a, a+b
Comparing the given polynomial with Ax³+Bx²+Cx+D=0
here A=2, B= -15 ,C=37 and D= -30
As we know that Sum of zero's = - B/A
a-b+a+a+b= - (-15)/2
3a= 15/2
a=5/2
Product of Zeros = -D/A
(a-b)a(a+b)= - (-30)/2
a[a²-b²]=15
Substituting the value of a in above equation, we get the value of b
[5/2][(5/2)²-b²]=15
25/4- b²=6
25-4b²=6x4
-4b²=24-25
-4b²=-1
b²=1/4
b= ±1/2
Zero's of polynomials are : a-b , a, a+b =5/2-1/2 , 5/2 , 5/2+1/2
=4/2 , 5/2, 6/2
=2, 5/2 ,3
Answer:
5/2, 1/2
Step-by-step explanation:
Now, using the relation between zeroes and the coefficients of the given cubic polynomial, we have:
Sum of roots = a - b + a + a + b = 15/ 2
=> 3a = 15/2
=> a = 5/2
Also,
Product of roots = (a - b) * a * (a + b) = 15
=> a(a² - b²) = 15
=> (5/2) * (a² - d²) = 15
=> d² = 1/4
=> d = 1/2
Therefore,
Zeroes are 5/2, 1/2
Hope it helps!