Question

the equation 2x^ + kx + 3 = 0 has 2 equal roots, than the value of k is :
a)+√6
b)+√4
c)+3√2
d)+2√6​

Answer 1

$\huge\bold{\underline{\sf{\pink{Answer}}}}$

$\huge\mathtt\red{2x² + kx + 3 = 0}$

$\mathrm\blue{Comparing \:equation \:with \:ax² + bx + c = 0}$

$\huge\mathtt\red{a = 2 \:b = k \:c = 3}$

$\mathrm\blue{\:Since \:the \:equation \:have \:2 \:equal \:root}$

$\mathrm\blue{\:So \:the \:discrimination \:[D] = 0}$

$\huge\mathtt\red{D = 0}$

$\huge\mathfrak\red{\:By \:using \:formula}$

${\green{\overline{\green{\underline{\blue{\boxed{\orange{\mathtt{b² - 4ac = 0}}}}}}}}}$

$\mathrm\blue{\:Substitute \:a , b , c \:value}$

$\huge\mathtt\red{K² = (-4) × 2 × 3 =0}$

$\huge\mathtt\red{K² = -24}$

$\huge\mathtt\red{K = ±√24}$

$\huge\mathtt\red{K = ±√6×4 }$

$\huge\mathtt\red{K = ±√6 × √4 }$

$\huge\mathtt\red{K = ±√6 × √2²}$

$\huge\mathtt\red{K = ±√6 × 2}$

$\huge\mathtt\red{K = ±2√6 }$

$\huge\bf\boxed{\boxed{\underline{\purple{Ans = (d)±2√6}}}}$

Answer 2

$\huge\bold{\underline{\sf{\pink{Answer}}}}$

$\huge\mathtt\red{2x² + kx + 3 = 0}$

$\mathrm\blue{Comparing \:equation \:with \:ax² + bx + c }$

$\huge\mathtt\red{a = 2 \:b = k \:c = 3}$

$\mathrm\blue{\:Since \:the \:equation \:have \:2 \:equal \:root}$

$\mathrm\blue{\:So \:the \:discrimination \:[D] = 0}$

$\huge\mathtt\red{D = 0}$

$\huge\mathfrak\red{\:By \:using \:formula}$

${\green{\overline{\green{\underline{\blue{\boxed{\orange{\mathtt{b² - 4ac = 0}}}}}}}}}$

$\mathrm\blue{\:Substitute \:a , b , c \:value}$

$\huge\mathtt\red{K² = (-4) × 2 × 3 =0}</p><p> \\ \\ \\ \\ </p><p>\huge\mathtt\red{K² = -24}</p><p> \\ \\ \\ </p><p>\huge\mathtt\red{K = ±√24}</p><p> \\ \\ \\ </p><p>\huge\mathtt\red{K = ±√6×4 }</p><p> \\ \\ \\ </p><p>\huge\mathtt\red{K = ±√6 × √4 }</p><p> \\ \\ \\ </p><p>\huge\mathtt\red{K = ±√6 × √2²}</p><p> \\ \\ \\ </p><p>\huge\mathtt\red{K = ±√6 × 2}</p><p> \\ \\ \\ </p><p>\huge\mathtt\red{K = ±2√6 }$

$\huge\bf\boxed{\boxed{\underline{\purple{Ans = (d)±2√6}}}}$