1.

Find the zeros , sum of zeros & product if zeros of 4√3x2+5x-2√3​

Answer»

ANSWER:

GIVEN:

  • P(x) = 4√3x²+5x-2√3

TO FIND:

  • Zeros , Sum of zeros , Product of the zeros.

SOLUTION:

=> 4√3x²+5x-2√3 = 0

=> 4√3x² +8x -3x -2√3 = 0

=> (4√3x²+8x)+(-3x-2√3) = 0

=> 4x(√3x+2) -√3(√3x+2) = 0

=> (√3x+2)(4x-√3) = 0

Either (√3x+2) = 0

=> √3x = -2

=> x = -2/√3

After rationalising :

=> x = -2√3/3

Either (4x-√3) = 0

=> 4x = √3

=> x = √3/4

Sum of zeros :

= \dfrac{ - 2 \sqrt{3} }{3} + \dfrac{ \sqrt{3} }{4} \\ \\ = \dfrac{ - 8 \sqrt{3} + 3 \sqrt{3} }{12} \\ \\ = \dfrac{ - 5 \sqrt{3} }{12}

Product of zeros:

= \dfrac{ - 2 \sqrt{3} }{3} \times \dfrac{ \sqrt{3} }{4} \\ \\ = \dfrac{ - 1}{2}

NOTE:

Some important formulas:

=> Sum of zeros (α+β) = -(Coefficient of x)/Coefficient of x²

=> Product of zeros (αβ) = CONSTANT TERM/ Coefficient of x²


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