If two of the zeros of the cubic polynomial ax3+bx2+cx+d are 0 then the third zero is a b/a b b/a c c/a d d/a
Open in App
Suggest Corrections
1
Let `alpha = 0, beta=0` and y be the zeros of the polynomial
f(x)= ax3 + bx2 + cx + d
Therefore
`alpha + ß + y= (-text{coefficient of }X^2)/(text{coefficient of } x^3)`
`= -(b/a)`
`alpha+beta+y = -b/a`
`0+0+y = -b/a`
`y = - b/a`
`\text{The value of} y - b/a`
Hence, the correct choice is `(c).`
Page 2
If two zeros x3 + x2 − 5x − 5 are \[\sqrt{5}\ \text{and} - \sqrt{5}\], then its third zero is
Let `alpha = sqrt5` and `beta= -sqrt5` be the given zeros and y be the third zero of x3 + x2 − 5x − 5 = 0 then
By using `alpha +beta + y = (-text{coefficient of }x^2)/(text{coefficient of } x^3)`
`alpha + beta + y = (+(+1))/1`
`alpha + beta + y = -1`
By substituting `alpha = sqrt5` and `beta= -sqrt5` in `alpha +beta+y = -1`
`cancel(sqrt5) - cancel(sqrt5) + y = -1`
` y = -1`
Hence, the correct choice is`(b)`
Concept: Relationship Between Zeroes and Coefficients of a Polynomial
Is there an error in this question or solution?
Page 3
Given `alpha, beta,y` be the zeros of the polynomial x3 + 4x2 + x − 6
Product of the zeros = `(\text{Constant term })/(\text{Coefficient of}\x^3) = (-(-6))/1 =6`
The value of Product of the zeros is 6.
Hence, the correct choice is `( c ).`
Text Solution
`(-b)/a` `b/a` `c/a` `(-d)/a`
Answer : A
Solution : Let ` alpha, 0, 0` be the zeros of `ax^(3) + bx^(2) + cx + d.` Then, <br> sum of zeros = `(-b)/a rArr alpha+0+0=(-b)/a rArr alpha = (-b)/a.` <br> Hence, the third zeros is `(-b)/a.`
Last updated at Dec. 4, 2021 by Teachoo
This video is only available for Teachoo black users
Introducing your new favourite teacher - Teachoo Black, at only ₹83 per month
Given, the cubic polynomial is ax³ + bx² + cx + d.
Two zeros of the polynomial are zero.
We have to find the third zero of the polynomial.
Let first zero be 𝛼, so 𝛼 = 0
Let second zero be ꞵ, so ꞵ = 0
We know that, if 𝛼, ꞵ and 𝛾 are the zeroes of a cubic polynomial ax³ + bx² + cx + d, then
Sum of the roots is 𝛼 + ꞵ + 𝛾 = -b/a
By the property, 0 + 0 + 𝛾 = -b/a
Therefore, the third zero is -b/a.
✦ Try This: Given that two of the zeroes of the cubic polynomial rx³ + sx² + tx + u are 0, the third zero is
Given, the cubic polynomial is rx³ + sx² + tx + u
Two zeros of the polynomial are zero
We have to find the third zero of the polynomial.
Let first zero be 𝛼, so 𝛼 = 0
Let second zero be ꞵ, so ꞵ = 0
We know that, if 𝛼, ꞵ and 𝛾 are the zeroes of a cubic polynomial ax³ + bx² + cx + d, then
Sum of the roots is 𝛼 + ꞵ + 𝛾 = -b/a
Here, a = r and b = s
By the property, 0 + 0 + 𝛾 = -b/a
𝛾 = -s/r
Therefore, the third zero is -s/r
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2
NCERT Exemplar Class 10 Maths Exercise 2.1 Solved Problem 2
Summary:
Given that the two zeros of the cubic polynomial ax³ + bx² + cx + d are zero, the third zero is -b/a
☛ Related Questions:
- A quadratic polynomial, whose zeroes are -3 and 4, is, a. x2 - x + 12, b. x2 + x + 12, c. x² /2 - x . . . .
- If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and -3, then a = -7, b = -1, a = . . . .
- The number of polynomials having zeroes as -2 and 5 is, a. 1, b. 2, c. 3, d. more than 3