Find the zeros of the following polynomials and the coefficients between the zeros and the coefficients of the polynomials. Relationship Verify: 4r + 5v2x-3
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Answer:
Let f(t)=5t
2
+12t+7
Comparing it with the standard quadratic polynomial ax
2
+bx+c, we get
a=5, b=12, c=7
Now, 5t
2
+12t+7
=5t
2
+5t+7t+7
=5t(t+1)+7(t+1)
=(t+1)(5t+7)
The zeros of f(t) are given by f(t)=0
=>(t+1)(5t+7)=0
=>t+1=0 or 5t+7=0
=>t=−1 or t=
5
−7
Hence the zeros of the given quadratic polynomial are −1,
5
−7
Verification of the relationship between the roots and the coefficients
Sum of the roots =−1+(
5
−7
)
=
5
−5−7
=
5
−12
=
coefficientofx
2
−coefficientofx
Product of the roots =−1×(
5
−7
)
Step-by-step explanation:
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