Given that the zeroes of the cubic polynomial x3-6x2+3x+10 are of the form a, a+b, q+2b, find the value of a and b as well as zeroes of the given polynomial.

Question

Answer

Given that a, a+b, a+2b are roots of given polynomial x^3-6x^2+3x+10From this polynomial,Sum of the roots ⇒ a+2b+a+a+b = -coefficient of x^2/ coefficient of x^3 ⇒ 3a+3b = -(-6)/1 = 6 ⇒ 3(a+b) = 6 ⇒ a+b = 2 --------- (1) b = 2-aProduct of roots ⇒ (a+2b)(a+b)a = -constant/coefficient of x^3 ⇒ (a+b+b)(a+b)a = -10/1Placing the value of a+b=2 in it ⇒ (2+b)(2)a = -10 ⇒ (2+b)2a = -10 ⇒ (2+2-a)2a = -10 ⇒ (4-a)2a = -10 ⇒ 4a-a^2 = -5 ⇒ a^2-4a-5 = 0 ⇒ a^2-5a+a-5 = 0 ⇒ (a-5)(a+1) = 0 a-5 = 0 or a+1 = 0 a = 5 a = -1  a = 5, -1 in (1) a+b = 2When a = 5, 5+b=2 ⇒ b=-3 a = -1, -1+b=2 ⇒ b= 3Therefore If a=5 then b= -3 or If a= -1 then b=3

Answer

Answer

Given that the zeroes of the cubic polynomial x3-6x2+3x+10 are of the form a, a+b, q+2b, find the value of a and b as well a

Answer

Substitute , once a,and once a+b and lastly q+2b equate to zero ,like this .a³-+a²+3a+10=0(a+b)³-6(a+b)²+3(a+b)=0and last one you will get answer .

Answer

130

Answer

Given Information:
The cubic polynomial is given as x^3 - 6x^2 + 3x + 10.
The zeroes of the polynomial follow a specific pattern: a, a + b, q + 2b, where a and b are unknown values.

Step 1: Finding the Value of 'a'
To find the value of 'a', we need to look at the coefficient of the x^2 term, which is -6 in this case.
According to the given pattern, the sum of the zeroes of the polynomial is equal to the opposite of the coefficient of the x^2 term.
So, a + (a + b) + (q + 2b) = -6

Simplifying the equation:
2a + 3b + q = -6

Step 2: Finding the Value of 'b'
To find the value of 'b', we need to look at the coefficient of the x term, which is 3 in this case.
According to the given pattern, the product of the zeroes taken two at a time is equal to the opposite of the coefficient of the x term.
So, a(a + b) + a(q + 2b) + (a + b)(q + 2b) = 3

Simplifying the equation:
3a^2 + 11ab + 3b^2 + aq + 2bq = 3

Step 3: Solving the Equations
Now, we have two equations with two unknowns:
2a + 3b + q = -6 ...(Equation 1)
3a^2 + 11ab + 3b^2 + aq + 2bq = 3 ...(Equation 2)

We can solve these equations simultaneously to find the values of 'a' and 'b'.

Step 4: Finding Zeroes of the Polynomial
Once we have the values of 'a' and 'b', we can substitute them back into the given pattern to find the zeroes of the polynomial.

The zeroes of the polynomial are:
a, a + b, q + 2b

Summary:
To find the values of 'a' and 'b', we solved the simultaneous equations obtained from the given pattern of zeroes. Then, we substituted the values of 'a' and 'b' back into the pattern to find the zeroes of the cubic polynomial x^3 - 6x^2 + 3x + 10.

Similar Class 10 Doubts

Anyone solve plz.zeroes of cubic polynomial X3-6X2 +3X+ 10 are of form a,a b,a-b . Find a and b and zeroes of polynomial also . where a and b are real values ?

Α, β, γ are zeroes of cubic polynomial x3 – 12x2 44x c. If α, β, γ are in AP, find the value of c.?

find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detaile d)?

If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q?

Top Courses for Class 10View all

Science Class 10

Mathematics (Maths) Class 10

Social Studies (SST) Class 10

English Class 10

Past Year Papers for Class 10

Top Courses for Class 10

Top Courses for Class 10

Related Content

About Class 10

Class 10 Study Material

Class 10 All Subjects

NCERT Textbook Solutions

Other Classes

Important Links

Company