Question

What is the sum of the roots of 3x²-4x-7=0

Answer 1

EXPLANATION.

Sum of the roots.

⇒ 3x² - 4x - 7 = 0.

As we know that,

Sum of the zeroes of the quadratic polynomial.

⇒ α + β = - b/a.

⇒ α + β = - (-4/3) = 4/3.

Products of the zeroes of the quadratic polynomial.

⇒ αβ = c/a.

⇒ αβ = (-7/3).

                                                                                                                 

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and unequal, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.

Answer 2

$\rm\large \bigstar \: {\underline{\underline\color{darkblue}{Given:-}}}$

$\rm \dashrightarrow{Sum \: of \: the \: roots = 3 {x}^{2} - 4x - 7 = 0.}$

$\rm\large \bigstar \: {\underline{\underline\color{darkblue}{Find:-}}}$

• Sum of the roots of 0 .

$\rm\large \bigstar \: {\underline{\underline\color{darkblue}{Solution:-}}}$

$\rm \mapsto{sum \: of \: the \: product \: of \: polynomial}$

$\rm\mapsto{a {x}^{2} +bx+c is \: given \: by  \frac{ - b}{a} \: . \: \frac{c}{a}. }$

Now,

$➛ \: \alpha \: + \beta = \frac{ - b}{c}$

$➛ \: \alpha + \beta \: = \: - ( \frac{4}{3} )$

$➛ \: \: \frac{4}{3}$

Now finding zeroes of the polynomial,

$➛ \: \alpha \: \beta = \frac{c}{a}$

$➛ \rm\purple { \: \: \alpha \: \beta = \frac{ - 7}{3}}$

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Learn more :-

$\begin{gathered} \: \: \: \: \: \: \begin{gathered}\boxed {\begin{array}{cc}\sf formula&\\\frac{\qquad }{ }{}\\\sf \: Sum = \frac{ - b}{a} &\ \\\\\sf roots = \frac{c}{a} &\\\\\sf \: Quadrtic \: equation = a {x}^{2} + bx + c = 0 \ \\ \\\sf Roots \: for \: quadrtic \: equation = \frac{ - b + - \sqrt{ {b}^{2} } - 4ac }{2a} &\end{array}}\end{gathered}\end{gathered}$

@Shivam