Question

obtain zeros of 4√3x^2+5x-2√3 and verify relation between its zeroes and coefficients​

Answer 1

Step-by-step explanation:

1. Find the zeros of the polynomial f(x) =4√3x²+5x-2√3 verify the relationship between the zeros & its coefficients?

The given polynomial f(x)

= 4√3 x^2 +5x - 2√3

= 4√3 x^2 + 8x - 3x - 2√3

= 4x(√3 x +2) - √3 (√3 x +2)

= (√3x+2)(4x-√3)

Hence the zeroes are -2/√3 and √3/4

Sum of the roots = -2/√3 + √3/4 = -2√3/3 + √3/4 = (-8√3+3√3)/12 = -5√3/12

Sum of the roots = -b/a = -5/4√3 = -5√3/12

Hence sum of the roots =-b/a.

Product of the roots = (-2/√3)(√3/4) = -1/2.

Product of the roots = c/a = -2√3/4√3 = -1/2.So product of the roots = c/a.

• Find the zeros of the polynomial f(x) =4√3x²+5x-2√3 verify the relationship between the zeros & its coefficients?
• The given polynomial f(x)
• = 4√3 x^2 +5x - 2√3
• = 4√3 x^2 + 8x - 3x - 2√3
• = 4x(√3 x +2) - √3 (√3 x +2)
• = (√3x+2)(4x-√3)
• Hence the zeroes are -2/√3 and √3/4
• Sum of the roots = -2/√3 + √3/4 = -2√3/3 + √3/4 = (-8√3+3√3)/12 = -5√3/12
• Sum of the roots = -b/a = -5/4√3 = -5√3/12
• Hence sum of the roots =-b/a.
• Product of the roots = (-2/√3)(√3/4) = -1/2.
• Product of the roots = c/a = -2√3/4√3 = -1/2.
• So product of the roots = c/a.
• Thus, the relationship between the roots and coefficients is verified.
• How can I find the zero of the polynomial for 4√3x^2+5x-2√3?
• How do you show that 1/2 and -3/2 are the zeros of polynomial for 4x^2 +3x + 2 and verify the relationship between zeros and coefficient?
• What are the zeroes of the following quadratic polynomial and verify the relationship between the zeros and coefficients of 2 √2x-9x+5√2?
• What are the zeros of the polynomial: 3x^3+3ax^2+6x+6a?
• What are the zeroes of the quadratic polynomial P(x) = 7x - 5x -2? What is the relationship between zeros and coefficients?
• f(x)=4.3–√.x2+5x−2.3–√
• Δ=(5)2+4(4)(2)(3–√)(3–√)=25+32×3=25+96=121=(11)2
• =>x1=−5+118.3√=68.3√
• =34.3√
• =3.3√4∗3
• =3√4
• And
• x2=−5−118.3√=−23√
• =−2.3√3
• We have x1+x2=54.3√=−b/a
• And x1.x2=−2.3√4.3√=c/a
• f(x)=ax2+bx+c
• Let its roots be p and q.
• So,
• P+q= -5/4√3. And pq= -2√3/4√3= -1/2
• Now, By Sridhar Acharya's formula*
• We can find p and q as:
• p=( -5+√(25–4(4√3)(-2√3)))/2(4√3)
• p=( -5+√(25+96))/8√3 = √3/4
• Thus q= -1/2p = -2/√3
• Sridhar Acharya's formula:
• For a quadratic eqn ax2+bx+c=0
• It's roots can be found as:
• x=(−b±√(b2−4ac))/(2a)
• So, first taking (+) you find first root and then taking (-) you take next root.
• Relation b/w roots and coefficients:
• Sum of roots = -b/a
• Product of roots= c/a
• Thank You
• f(x)=4√3x^2+5x-2√3
• = 4√3x^2+8x-3x-2√3
• = 4x(√3x+2)-√3(√3x+2).
• = (√3x+2).(4x-√3)
• Thus , zeros are -2/√3. and √3/4 .
• Let p and q are the zeroes of f(x)= 4√3.x^2+5x-2√3 ,
• Sum of the zeroes=p+q = -b/a =-5/4√3.
• -2/√3+√3/4= -5/4√3.
• or. (-8+3)/4√3=-5/4√3.
• or. -5/4√3. = -5/4√3. True.
• Product of the zeroes=p.q=c/a= -2√3/4√3
• (-2/√3)×(√3/4)=-1/2.
• or. -1/2= -1/2. True. Answer