If the product of the zeroes of the quadratic polynomial 3x² + 5x + k

1.	If the product of the zeroes of the quadratic polynomial 3x² + 5x + k is -2/3 , thenk = -3k = -2 k = 2k = 3
Answer» 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 _________________________________ 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 ________________________________

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

Answer»

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

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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