Question

Verify the relationship between the zeroes and the coefficients of the polynomial $p (x) = 3 x^{2} - 5 x$ .

Approach

Factorizing $p (x) = x (3 x - 5)$ gives zeroes $0$ and $\frac{5}{3}$ . Sum of zeroes = $0 + \frac{5}{3} = \frac{5}{3} = - \frac{( - 5 )}{3}$ . Product of zeroes = $0 \times \frac{5}{3} = 0 = \frac{0}{3}$ . Relationship verified.

Step-by-step working

1
Zeroes are $0$ and $\frac{5}{3}$
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2
Sum of zeroes = $0 + \frac{5}{3} = \frac{5}{3} = - \frac{coefficient of x}{coefficient of x ^{2}}$
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3
Product of zeroes = $0 \times \frac{5}{3} = 0 = \frac{constant term}{coefficient of x ^{2}}$
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4
Relationship verified
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Concepts used

zeroes of polynomialsum of rootsproduct of rootsverification

Approach

Step-by-step working

Concepts used

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