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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
Solution
Let the required roots be p ,q ,r let the two roots let p and q be 0 (given)
we know that→ sum of roots = -b/a
→ p + q + r = -b/a
→ 0 + 0 + r = -b/a
→ r = -(b/a)
so option a is correct
Mathematics
Secondary School Mathematics X
Standard X
0
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
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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 ).`