Question

If the product of the zeroes of the quadratic polynomial 3x² + 5x + k is -2/3 , then
k = -3
k = -2
k = 2
k = 3

Answer 1

Answer:

k = -2

Step-by-step explanation:

Given :

The product of the zeroes of the quadratic polynomial 3x² + 5x + k is -2/3

To find :

the value of k

Solution :

3x² + 5x + k

• x² coefficient = 3
• x coefficient = 5
• constant term = k

From the relation between zeroes and coefficients of the quadratic equation :

Product of zeroes = constant term/x² coefficient  

 $\sf \dfrac{-2}{3}=\dfrac{k}{3} \\\\ \sf k=\dfrac{-2}{3} \times 3 \\\\ \sf k=-2$

Therefore, the value of k is -2

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About Quadratic Polynomial :    

✯ It is a polynomial of degree 2    

✯ General form :    

 ax² + bx + c  = 0    

✯ Determinant, D = b² - 4ac    

✯ Based on the value of Determinant, we can define the nature of roots.    

D > 0 ; real and unequal roots    

D = 0 ; real and equal roots    

D < 0 ; no real roots i.e., imaginary    

✯ Relationship between zeroes and coefficients :    

✩ Sum of zeroes = -b/a    

✩ Product of zeroes = c/a    

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Answer 2

$\cal\huge{Given\::} \\ \\ \Rightarrow\text{If the product of the zeroes} \\ \text{of the quadratic polynomial} \\ \text{3x² + 5x + k is -2/3.} \\ \\ \\ \cal\huge{To\:Find\::} \\ \\ \text{• k = ? or value of k}\\ \\ \huge\cal\red{S} \huge\cal\blue{o} \huge\cal\green{l} \huge\cal\purple{u} \huge\cal\orange{t} \huge\cal\red{i} \huge\cal\blue{o} \huge\cal\green{n} \huge\cal\purple{:} \\ \\ \text{We also know that :} \\ \text{3 = x² cofficient} \\ \text{5 = x cofficient} \\ \text{k = constant} \\ \\ \text{We know that :} \\ Product\:of\:zeroes\,=\, \frac{constant}{x²} \\ \\ \frac{-2}{3} = \frac{k}{3} \\ So,\;k\,=\, \frac{-2}{3} \times 3 \\ \\ \text{3 and 3 get cancelled, and} \\ \text{Therefore, \bf\red{k =} \bf\red{-2}.} \\ \\\text\blue{Hope it will help you..}$